what is the minimum speed the student must have to just catch up with the bus?
Problem 1
A car travels in the $+x$-direction on a straight and level road. For the first iv.00 southward of its motion, the average velocity of the machine is $v_{av-x}$ = half-dozen.25 chiliad/s. How far does the car travel in 4.00 south?
Kahlan Grand.
Numerade Educator
Problem ii
In an experiment, a shearwater (a seabird) was taken from its nest, flown 5150 km away, and released. The bird found its manner back to its nest xiii.5 days after release. If nosotros place the origin at the nest and extend the +$x$-axis to the release indicate, what was the bird'south average velocity in m/due south (a) for the return flight and (b) for the whole episode, from leaving the nest to returning?
Gilbert Fifty.
University of California, Berkeley
Problem three
You unremarkably drive on the state highway between San Diego and Los Angeles at an average speed of 105 km/h (65 mi/h), and the trip takes 1 h and 50 min. On a Friday afternoon, however, heavy traffic slows you downwardly and y'all drive the aforementioned altitude at an average speed of only 70 km/h (43 mi/h). How much longer does the trip take?
Ryan H.
Numerade Educator
Problem 4
Starting from a pillar, you run 200 one thousand east (the $+10$-direction) at an average speed of 5.0 m/south and and then run 280 1000 west at an boilerplate speed of 4.0 yard/due south to a postal service. Calculate (a) your average speed from pillar to post and (b) your average velocity from colonnade to mail.
Johnny G.
University of Minnesota - Twin Cities
Problem five
Starting from the front door of a ranch house, y'all walk 60.0 m due east to a windmill, plow around, and then slowly walk twoscore.0 m due west to a bench, where you sit and watch the sunrise. It takes you 28.0 due south to walk from the house to the windmill and then 36.0 s to walk from the windmill to the bench. For the entire trip from the front door to the demote, what are your (a) average velocity and (b) boilerplate speed?
Ryan H.
Numerade Educator
Problem half dozen
A Honda Civic travels in a straight line along a route. The car's distance $x$ from a finish sign is given as a function of time $t$ by the equation $x(t) = \blastoff{t^ii} - \beta{t^3}$, where $\alpha =$ 1.50 m/s$^2$ and $\beta =$ 0.0500 one thousand/s$^3$. Calculate the average velocity of the auto for each time interval: (a) $t =$ 0 to $t =$ 2.00 s; (b) $t =$ 0 to $t =$ iv.00 due south; (c) $t =$ 2.00 s to $t =$ 4.00 southward.
Johnny Thousand.
Academy of Minnesota - Twin Cities
Problem 7
A car is stopped at a traffic light. It and so travels along a straight route such that its distance from the light is given by $x(t) = bt^2 - ct^3$, where $b =$ 2.xl thou/southward$^2$ and $c =$ 0.120 m/s$^three$. (a) Calculate the average velocity of the machine for the fourth dimension interval $t =$ 0 to $t =$ 10.0 s. (b) Calculate the instantaneous velocity of the car at $t =$ 0, $t =$ 5.0 s, and $t =$ 10.0 s. (c) How long after starting from rest is the car again at rest?
Ryan H.
Numerade Educator
Problem 8
A bird is flying due eastward. Its distance from a tall building is given by $10(t) =$ 28.0 one thousand $+$ (12.4 m/s)$t$ - (0.0450 m/southward$^3)t^3$. What is the instantaneous velocity of the bird when $t =$ viii.00 due south?
Johnny G.
University of Minnesota - Twin Cities
Problem 9
A ball moves in a direct line (the $x$-axis). The graph in $\textbf{Fig. E2.9}$ shows this ball's velocity as a office of fourth dimension. (a) What are the ball's average speed and average velocity during the showtime 3.0 south? (b) Suppose that the ball moved in such a manner that the graph segment after 2.0 s was $-$3.0 m/due south instead of $+$3.0 m/s. Find the brawl'south average speed and average velocity in this case.
Ryan H.
Numerade Educator
Trouble 10
A physics professor leaves her house and walks along the sidewalk toward campus. After five min it starts to rain, and she returns dwelling house. Her distance from her firm as a part of fourth dimension is shown in $\textbf{Fig. E2.10}.$ At which of the labeled points is her velocity (a) goose egg? (b) constant and positive? (c) constant and negative? (d) increasing in magnitude? (e) decreasing in magnitude?
Johnny G.
Academy of Minnesota - Twin Cities
Problem xi
A test car travels in a straight line along the $10$-axis. The graph in $\textbf{Fig. E2.xi}$ shows the car'southward position $10$ as a office of time. Detect its instantaneous velocity at points $A$ through $G$.
Ryan H.
Numerade Educator
Problem 12
Figure $\mathrm{E} 2.12$ shows the velocity of a solar-powered auto as a office of time. The commuter accelerates from a stop sign, cruises for $20 \mathrm{~s}$ at a constant speed of $60 \mathrm{~km} / \mathrm{h},$ and then brakes to come to a finish $40 \mathrm{~due south}$ after leaving the stop sign. (a) Compute the average dispatch during these time intervals:
(i) $t=0$ to $t=10 \mathrm{~s} ;$ (ii) $t=30 \mathrm{~s}$ to $t=40 \mathrm{~s} ;$ (3) $t=10 \mathrm{~s}$ to $t=30 \mathrm{~s}$ (four) $t=0$ to $t=40 \mathrm{~s}$. (b) What is the instantaneous acceleration at $t=20 \mathrm{~s}$ and at $t=35 \mathrm{~s} ?$
Gilbert L.
University of California, Berkeley
Problem 13
The table shows test data for the Bugatti Veyron Super Sport, the fastest street car fabricated. The machine is moving in a straight line (the $10$-axis). (a) Sketch a $v_x-t$ graph of this car'south velocity (in mi/h) as a function of time. Is its dispatch constant? (b) Calculate the car's boilerplate acceleration (in thousand/south$^ii$) between (i) 0 and 2.1 s; (two) 2.1 southward and twenty.0 due south; (iii) twenty.0 s and 53 s. Are these results consequent with your graph in part (a)? (Before yous decide to buy this car, it might be helpful to know that only 300 will exist congenital, it runs out of gas in 12 minutes at pinnacle speed, and it costs more than than $1.v 1000000!)
Ryan H.
Numerade Educator
Problem fourteen
A race machine starts from balance and travels e along a straight and level track. For the kickoff 5.0 south of the automobile's motion, the eastward component of the machine'southward velocity is given by $v_x(t) =$ 0.860 m/s$^3)t^2$. What is the acceleration of the car when $v_x =$ 12.0 m/s?
Johnny G.
University of Minnesota - Twin Cities
Problem 15
A turtle crawls along a straight line, which we volition call the $x$-axis with the positive direction to the right. The equation for the turtle's position as a function of time is $x(t) =$ l.0 cm + (two.00 cm/s)$t -$ (0.0625 cm/due south$^2)t^2$. (a) Find the turtle's initial velocity, initial position, and initial dispatch. (b) At what time $t$ is the velocity of the turtle nada? (c) How long after starting does it take the turtle to render to its starting point? (d) At what times $t$ is the turtle a distance of 10.0 cm from its starting point? What is the velocity (magnitude and direction) of the turtle at each of those times? (e) Sketch graphs of $10$ versus $t, v_x$ versus $t$, and $a_x$ versus $t$, for the fourth dimension interval $t =$ 0 to $t =$ 40 s.
Ryan H.
Numerade Educator
Problem 16
An astronaut has left the International Space Station to examination a new infinite scooter. Her partner measures the post-obit velocity changes, each taking place in a 10-south interval. What are the magnitude, the algebraic sign, and the direction of the average acceleration in each interval? Presume that the positive direction is to the correct. (a) At the beginning of the interval, the astronaut is moving toward the right forth the $x$-axis at fifteen.0 yard/s, and at the end of the interval she is moving toward the right at 5.0 k/southward. (b) At the start she is moving toward the left at v.0 m/due south, and at the stop she is moving toward the left at fifteen.0 m/southward. (c) At the outset she is moving toward the right at xv.0 one thousand/south, and at the finish she is moving toward the left at fifteen.0 m/due south.
Johnny Yard.
University of Minnesota - Twin Cities
Problem 17
A automobile'south velocity as a function of time is given past $v_x(t) = \alpha + \beta t^2$, where $\alpha =$ iii.00 m/due south and $\beta =$ 0.100 grand/southward$^3$. (a) Calculate the average acceleration for the fourth dimension interval $t =$ 0 to $t =$ 5.00 s. (b) Calculate the instantaneous acceleration for $t =$ 0 and $t =$ 5.00 due south. (c) Draw $v_x-t$ and $a_x-t$ graphs for the auto's move between $t =$ 0 and $t =$ 5.00 southward.
Ryan H.
Numerade Educator
Problem xviii
The position of the front bumper of a examination automobile nether microprocessor command is given by $x(t) =$ 2.17 k $+$ (4.eighty m/due south$^2)t^ii$ $-$ (0.100 grand/s$^6)t^6$. (a) Find its position and dispatch at the instants when the auto has zero velocity. (b) Describe $x-t, v_x-t$, and $a_x-t$ graphs for the move of the bumper between $t =$ 0 and $t =$ 2.00 s.
Johnny G.
University of Minnesota - Twin Cities
Problem 19
An antelope moving with abiding dispatch covers the distance between ii points 70.0 m apart in 6.00 south. Its speed as it passes the second point is 15.0 m/south. What are (a) its speed at the first point and (b) its acceleration?
Ryan H.
Numerade Educator
Problem 20
A jet fighter pilot wishes to accelerate from residue at a abiding acceleration of 5$g$ to reach Mach 3 (three times the speed of sound) every bit quickly every bit possible. Experimental tests reveal that he will black out if this acceleration lasts for more 5.0 south. Employ 331 m/southward for the speed of sound. (a) Will the period of acceleration last long enough to cause him to black out? (b) What is the greatest speed he can reach with an acceleration of five$one thousand$ before he blacks out?
Johnny G.
University of Minnesota - Twin Cities
Problem 21
The fastest measured pitched baseball left the pitcher's hand at a speed of 45.0 m/s. If the bullpen was in contact with the ball over a distance of 1.50 m and produced constant dispatch, (a) what acceleration did he give the brawl, and (b) how much time did information technology have him to pitch it?
Ryan H.
Numerade Educator
Trouble 22
In the fastest measured tennis serve, the ball left the racquet at 73.xiv m/s. A served tennis ball is typically in contact with the racquet for 30.0 ms and starts from residuum. Assume constant dispatch. (a) What was the ball'due south acceleration during this serve? (b) How far did the brawl travel during the serve?
Johnny Chiliad.
Academy of Minnesota - Twin Cities
Trouble 23
The man trunk can survive an acceleration trauma incident (sudden terminate) if the magnitude of the acceleration is less than 250 m/s$^{ii}$. If y'all are in an car accident with an initial speed of 105 km/h (65 mi/h) and are stopped by an airbag that inflates from the dashboard, over what altitude must the airbag stop you for you to survive the crash?
Ryan H.
Numerade Educator
Problem 24
A pilot who accelerates at more 4$k$ begins to "gray out" but doesn't completely lose consciousness. (a) Assuming constant dispatch, what is the shortest fourth dimension that a jet pilot starting from remainder tin take to reach Mach 4 (4 times the speed of sound) without graying out? (b) How far would the aeroplane travel during this period of acceleration? (Apply 331 g/s for the speed of audio in cold air.)
Johnny G.
University of Minnesota - Twin Cities
Trouble 25
During an auto accident, the vehicle's air bags deploy and deadening down the passengers more than gently than if they had hit the windshield or steering wheel. According to condom standards, air bags produce a maximum dispatch of $60 g$ that lasts for merely $36 \mathrm{~ms}$ (or less). How far (in meters) does a person travel in coming to a complete stop in $36 \mathrm{~ms}$ at a constant acceleration of $60 \mathrm{~g} ?$
Ryan H.
Numerade Educator
Problem 26
$\textbf{Prevention of Hip Fractures.}$ Falls resulting in hip fractures are a major crusade of injury and even death to the elderly. Typically, the hip's speed at bear on is well-nigh ii.0 m/s. If this can be reduced to one.3 m/southward or less, the hip will usually not fracture. One style to do this is by wearing elastic hip pads. (a) If a typical pad is five.0 cm thick and compresses by 2.0 cm during the bear on of a fall, what abiding dispatch (in m/due south$^{two}$ and in $\text{thou}$'s) does the hip undergo to reduce its speed from ii.0 m/s to 1.iii grand/s? (b) The dispatch you found in part (a) may seem rather large, but to assess its effects on the hip, summate how long it lasts.
Johnny G.
University of Minnesota - Twin Cities
Trouble 27
Information technology has been suggested, and not facetiously, that life might have originated on Mars and been carried to the earth when a falling star hit Mars and blasted pieces of stone (possibly containing archaic life) costless of the Martian surface. Astronomers know that many Martian rocks have come up to the earth this way. (For instance, search the Internet for "ALH 84001.") One objection to this idea is that microbes would accept had to undergo an enormous lethal acceleration during the impact. Let us investigate how big such an acceleration might be. To escape Mars, rock fragments would have to reach its escape velocity of 5.0 km/s, and that would most likely happen over a distance of nigh 4.0 m during the meteor impact. (a) What would exist the acceleration (in g/s$^ii$ and $g'$south) of such a rock fragment, if the acceleration is constant? (b) How long would this acceleration last? (c) In tests, scientists have found that over 40$\text{%}$ of $\textit{Bacillus subtilis}$ bacteria survived later an dispatch of 450,000$g$. In calorie-free of your answer to function (a), can we rule out the hypothesis that life might have been blasted from Mars to the earth?
Ryan H.
Numerade Educator
Problem 28
A car sits on an entrance ramp to a freeway, waiting for a break in the traffic. Then the commuter accelerates with constant acceleration along the ramp and onto the freeway. The auto starts from rest, moves in a straight line, and has a speed of 20 m/s (45 mi/h) when it reaches the stop of the 120-one thousand-long ramp. (a) What is the dispatch of the auto? (b) How much time does it have the car to travel the length of the ramp? (c) The traffic on the freeway is moving at a constant speed of 20 1000/s. What distance does the traffic travel while the auto is moving the length of the ramp?
Johnny Grand.
University of Minnesota - Twin Cities
Problem 29
At launch a rocket send weighs 4.5 million pounds. When it is launched from residuum, information technology takes 8.00 southward to achieve 161 km/h; at the stop of the start 1.00 min, its speed is 1610 km/h. (a) What is the average acceleration (in one thousand/south$^ii$) of the rocket (i) during the first 8.00 s and (ii) between 8.00 south and the end of the first 1.00 min? (b) Bold the acceleration is constant during each time interval (but not necessarily the same in both intervals), what distance does the rocket travel (i) during the first 8.00 s and (ii) during the interval from 8.00 south to 1.00 min?
Ryan H.
Numerade Educator
Trouble xxx
A true cat walks in a straight line, which we shall phone call the $x$-axis, with the positive direction to the correct. As an observant physicist, yous make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time ($\textbf{Fig. E2.xxx}$). (a) Find the cat's velocity at $t =$ 4.0 s and at $t =$ vii.0 southward. (b) What is the cat's acceleration at $t =$ iii.0 s? At $t =$ 6.0 southward ? At $t =$ 7.0 s ? (c) What distance does the cat move during the first 4.5 s? From $t =$ 0 to $t =$ 7.5 s ? (d) Assuming that the cat started at the origin, sketch clear graphs of the cat's acceleration and position as functions of time.
Johnny G.
Academy of Minnesota - Twin Cities
Problem 31
The graph in $\textbf{Fig. E2.31}$ shows the velocity of a motorcycle police officeholder plotted as a role of time. (a) Discover the instantaneous acceleration at $t =$ 3 s, $t =$ 7 s, and $t =$ 11 s. (b) How far does the officeholder go in the first 5 s? The beginning 9 s? The outset 13 s?
Ryan H.
Numerade Educator
Problem 32
Two cars, $A$ and $B$, move along the $x$-axis. $\textbf{Figure E2.32}$ is a graph of the positions of $A$ and $B$ versus time. (a) In motion diagrams (like Figs. two.13b and 2.14b), show the position, velocity, and acceleration of each of the two cars at $t =$ 0, $t =$ 1 s, and $t =$ 3 s. (b) At what fourth dimension(s), if any, do $A$ and $B$ have the same position? (c) Graph velocity versus time for both $A$ and $B$. (d) At what time(south), if whatever, do $A$ and $B$ accept the same velocity? (e) At what time(south), if any, does car $A$ pass car $B$? (f) At what fourth dimension(due south), if whatever, does automobile $B$ pass car $A$?
Johnny M.
University of Minnesota - Twin Cities
Problem 33
A small block has abiding acceleration equally it slides down a frictionless incline. The block is released from residue at the top of the incline, and its speed subsequently it has traveled 6.80 m to the bottom of the incline is 3.80 k/s. What is the speed of the block when information technology is 3.40 g from the acme of the incline?
Ryan H.
Numerade Educator
Problem 34
At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant dispatch of ii.80 m/s$^ii$. At the aforementioned instant a truck, traveling with a constant speed of 20.0 m/due south, overtakes and passes the car. (a) How far beyond its starting point does the car overtake the truck? (b) How fast is the motorcar traveling when it overtakes the truck? (c) Sketch an $x-t$ graph of the motion of both vehicles. Take $x=$ 0 at the intersection. (d) Sketch a $v_x-t$ graph of the motion of both vehicles.
Johnny G.
University of Minnesota - Twin Cities
Problem 35
(a) If a flea can spring straight up to a elevation of 0.440 k, what is its initial speed equally it leaves the ground? (b) How long is information technology in the air?
Ryan H.
Numerade Educator
Trouble 36
A minor rock is thrown vertically upwardly with a speed of 22.0 m/southward from the edge of the roof of a xxx.0-g-tall building. The rock doesn't striking the edifice on its way back downwards and lands on the street beneath. Ignore air resistance. (a) What is the speed of the rock simply earlier it hits the street? (b) How much time elapses from when the rock is thrown until information technology hits the street?
Johnny G.
Academy of Minnesota - Twin Cities
Problem 37
A juggler throws a bowling pin straight upward with an initial speed of 8.twenty k/s. How much time elapses until the bowling pin returns to the juggler's hand?
Priyanka K.
Numerade Educator
Trouble 38
Y'all throw a glob of putty straight upwards toward the ceiling, which is 3.lx m to a higher place the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is 9.50 thousand/s. (a) What is the speed of the putty just before it strikes the ceiling? (b) How much time from when it leaves your hand does information technology have the putty to attain the ceiling?
Johnny One thousand.
University of Minnesota - Twin Cities
Problem 39
A tennis ball on Mars, where the acceleration due to gravity is 0.379$grand$ and air resistance is negligible, is hitting directly upward and returns to the aforementioned level 8.5 due south subsequently. (a) How loftier to a higher place its original point did the ball go? (b) How fast was it moving just after it was hit? (c) Sketch graphs of the ball'south vertical position, vertical velocity, and vertical acceleration equally functions of time while it'due south in the Martian air.
Ryan H.
Numerade Educator
Trouble 40
A lunar lander is making its descent to Moon Base I ($\textbf{Fig. E2.40}$). The lander descends slowly under the retro-thrust of its descent engine. The engine is cut off when the lander is 5.0 thousand above the surface and has a downward speed of 0.8 m/s.With the engine off, the lander is in gratuitous fall. What is the speed of the lander just before it touches the surface? The acceleration due to gravity on the moon is one.6 m/s$^{2}$.
Johnny G.
University of Minnesota - Twin Cities
Trouble 41
A meter stick is held vertically to a higher place your hand, with the lower end between your pollex and first finger. When you see the meter stick released, you lot grab information technology with those two fingers. Yous can calculate your reaction time from the distance the meter stick falls, read straight from the betoken where your fingers grabbed information technology. (a) Derive a relationship for your reaction fourth dimension in terms of this measured altitude, $d$. (b) If the measured distance is 17.6 cm, what is your reaction time?
Ryan H.
Numerade Educator
Trouble 42
A brick is dropped (zippo initial speed) from the roof of a building. The brick strikes the ground in ane.90 southward. You lot may ignore air resistance, then the brick is in complimentary autumn. (a) How tall, in meters, is the edifice? (b) What is the magnitude of the brick's velocity merely earlier it reaches the ground? (c) Sketch $a_y-t, v_y-t$, and $y-t$ graphs for the motion of the brick.
Johnny G.
University of Minnesota - Twin Cities
Problem 43
A 7500-kg rocket blasts off vertically from the launch pad with a constant upward dispatch of two.25 thousand/s$^2$ and feels no appreciable air resistance. When information technology has reached a height of 525 m, its engines all of a sudden fail; the but force acting on it is now gravity. (a) What is the maximum tiptop this rocket volition reach above the launch pad? (b) How much fourth dimension volition elapse after engine failure before the rocket comes crashing down to the launch pad, and how fast will it be moving merely earlier information technology crashes? (c) Sketch $a_y-t, v_y-t$, and $y-t$ graphs of the rocket's motility from the instant of blast-off to the instant merely before it strikes the launch pad.
Ryan H.
Numerade Educator
Problem 44
A hot-air balloonist, rising vertically with a constant velocity of magnitude 5.00 yard/s, releases a sandbag at an instant when the balloon is 40.0 one thousand above the footing ($\textbf{Fig. E2.44}$). After the sandbag is released, information technology is in gratis fall. (a) Compute the position and velocity of the sandbag at 0.250 s and 1.00 s after its release. (b) How many seconds after its release does the purse strike the basis? (c) With what magnitude of velocity does information technology strike the ground? (d) What is the greatest superlative above the ground that the sandbag reaches? (e) Sketch $a_y-t$, $v_y-t$, and $y-t$ graphs for the movement.
Johnny M.
Academy of Minnesota - Twin Cities
Problem 45
The rocket-driven sled $\textit{Sonic Wind No. 2,}$ used for investigating the physiological effects of big accelerations, runs on a straight, level track 1070 m (3500 ft) long. Starting from rest, it can achieve a speed of 224 thousand/s(500 mi/h) in 0.900 s. (a) Compute the acceleration in 1000/southward$^two$, assuming that it is abiding. (b) What is the ratio of this acceleration to that of a freely falling body ($1000$)? (c) What distance is covered in 0.900 s? (d) A magazine article states that at the end of a certain run, the speed of the sled decreased from 283 m/s (632 mi/h) to zilch in 1.40 s and that during this time the magnitude of the acceleration was greater than 40$g$. Are these figures consistent?
Ryan H.
Numerade Educator
Problem 46
An egg is thrown nearly vertically upward from a point near the cornice of a alpine building. The egg just misses the cornice on the way down and passes a point 30.0 m below its starting point 5.00 s after it leaves the thrower'south mitt. Ignore air resistance. (a) What is the initial speed of the egg? (b) How high does it rise to a higher place its starting point? (c) What is the magnitude of its velocity at the highest point? (d) What are the magnitude and direction of its acceleration at the highest point? (eastward) Sketch $a_y-t, v_y-t$, and $y-t$ graphs for the motility of the egg.
Johnny G.
University of Minnesota - Twin Cities
Problem 47
A 15-kg stone is dropped from rest on the earth and reaches the ground in one.75 s. When it is dropped from the same height on Saturn's satellite Enceladus, the rock reaches the footing in 18.6 south. What is the dispatch due to gravity on Enceladus?
Ryan H.
Numerade Educator
Problem 48
A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 1000/s. Ignore air resistance. (a) At what time after being ejected is the boulder moving at 20.0 m/south upward? (b) At what time is it moving at 20.0 1000/southward downward? (c) When is the displacement of the boulder from its initial position zero? (d) When is the velocity of the boulder cypher? (e) What are the magnitude and direction of the acceleration while the boulder is (i) moving upward? (two) Moving downward? (iii) At the highest
point? (f) Sketch $a_y-t, v_y-t$, and $y-t$ graphs for the motility.
Johnny G.
University of Minnesota - Twin Cities
Trouble 49
You throw a small stone straight up from the edge of a highway bridge that crosses a river. The stone passes you on its manner downward, six.00 southward later on it was thrown. What is the speed of the rock just before it reaches the water 28.0 m beneath the point where the stone left your hand? Ignore air resistance.
Ryan H.
Numerade Educator
Trouble 50
A small object moves along the $x$ -centrality with dispatch $a_{x}(t)=-\left(0.0320 \mathrm{~m} / \mathrm{southward}^{3}\right)(15.0 \mathrm{~south}-t) .$ At $t=0$ the object is at $10=-14.0 \mathrm{~m}$ and has velocity $v_{0 ten}=eight.00 \mathrm{~m} / \mathrm{s} .$ What is the $x$ -coordinate of the object when $t=ten.0 \mathrm{~s} ?$
Johnny G.
Academy of Minnesota - Twin Cities
Problem 51
A rocket starts from rest and moves upward from the surface of the earth. For the first x.0 south of its motion, the vertical acceleration of the rocket is given by $a_y =$ (2.80 m/s$^iii)t$, where the $+y$-management is upward. (a) What is the height of the rocket above the surface of the globe at $t =$ 10.0 s? (b) What is the speed of the rocket when it is 325 m above the surface of the earth?
Ryan H.
Numerade Educator
Problem 52
The acceleration of a bus is given by $a_{x}(t)=\blastoff t$ where $\alpha=1.2 \mathrm{~m} / \mathrm{s}^{iii} .$ (a) If the bus's velocity at fourth dimension $t=1.0 \mathrm{~s}$ is $5.0 \mathrm{~1000} / \mathrm{s},$ what is its velocity at fourth dimension $t=2.0 \mathrm{~s} ?$ (b) If the charabanc'due south position at fourth dimension $t=i.0 \mathrm{~due south}$ is $6.0 \mathrm{~m},$ what is its position at time $t=2.0 \mathrm{~s} ?$ (c) Sketch $a_{y}-t, v_{y}-t,$ and $10-t$ graphs for the move.
Johnny M.
University of Minnesota - Twin Cities
Trouble 53
The acceleration of a motorcycle is given past $a_x(t) = At - Bt^2$ where $A =$ 1.50 m/s$^3$ and $B$ = 0.120 m/due south$^four$. The motorcycle is at rest at the origin at time $t =$ 0. (a) Find its position and velocity as functions of fourth dimension. (b) Calculate the maximum velocity it attains.
Ryan H.
Numerade Educator
Problem 54
High-speed motion pictures (3500 frames/2nd) of a jumping, 210-$\mu$g flea yielded the data used to plot the graph in $\textbf{Fig. E2.54.}$ (See "The Flying Jump of the Flea" by M. Rothschild, Y. Schlein, K. Parker, C. Neville, and S. Sternberg in the November 1973 $Scientific American$.) This flea was about 2 mm long and jumped at a virtually vertical takeoff angle. Use the graph to respond these questions: (a) Is the dispatch of the flea e'er cipher? If then, when? Justify your respond. (b) Find the maximum elevation the flea reached in the first two.5 ms. (c) Find the flea'southward acceleration at 0.5 ms, 1.0 ms, and i.five ms. (d) Find the flea's height at 0.5 ms, i.0 ms, and 1.5 ms.
Johnny G.
Academy of Minnesota - Twin Cities
Problem 55
A typical male sprinter can maintain his maximum acceleration for 2.0 south, and his maximum speed is 10 k/s. After he reaches this maximum speed, his acceleration becomes zero, and then he runs at constant speed. Presume that his acceleration is constant during the first 2.0 due south of the race, that he starts from rest, and that he runs in a straight line. (a) How far has the sprinter run when he reaches his maximum speed? (b) What is the magnitude of his average velocity for a race of these lengths: (i) l.0 m; (ii) 100.0 chiliad; (iii) 200.0 g?
Ryan H.
Numerade Educator
Problem 56
A lunar lander is descending toward the moon'due south surface. Until the lander reaches the surface, its peak above the surface of the moon is given by $y(t) = b - ct + dt^two$ , where $b =$ 800 g is the initial height of the lander to a higher place the surface, $c =$ 60.0 m/s, and $d =$ one.05 m/s$^ii$. (a) What is the initial velocity of the lander, at $t =$ 0? (b) What is the velocity of the lander simply earlier it reaches the lunar surface?
Johnny Grand.
Academy of Minnesota - Twin Cities
Problem 57
Earthquakes produce several types of shock waves. The most well known are the P-waves (P for $primary$ or $force per unit area$) and the S-waves (Southward for $secondary$ or $shear$). In the earth'due south crust, P-waves travel at nearly 6.5 km/southward and S-waves move at about 3.5 km/southward. The fourth dimension delay between the arrival of these two waves at a seismic recording station tells geologists how far abroad an convulsion occurred. If the time delay is 33 southward, how far from the seismic station did the earthquake occur?
Ryan H.
Numerade Educator
Problem 58
A brick is dropped from the roof of a tall building. After information technology has been falling for a few seconds, it falls 40.0 m in a 1.00-southward fourth dimension interval. What distance will information technology fall during the next 1.00 south? Ignore air resistance.
Johnny Chiliad.
University of Minnesota - Twin Cities
Problem 59
A rocket carrying a satellite is accelerating straight upwardly from the earth's surface. At 1.fifteen south after liftoff, the rocket clears the tiptop of its launch platform, 63 m above the ground. Later an additional 4.75 s, it is 1.00 km higher up the ground. Calculate the magnitude of the average velocity of the rocket for (a) the iv.75-s part of its flight and (b) the starting time 5.90 s of its flight.
Ryan H.
Numerade Educator
Problem lx
A subway railroad train starts from balance at a station and accelerates at a rate of 1.60 g/s$^2$ for fourteen.0 s. It runs at constant speed for 70.0 s and slows down at a rate of 3.50 m/southward$^2$ until it stops at the next station. Find the total distance covered.
Johnny K.
Academy of Minnesota - Twin Cities
Problem 61
A gazelle is running in a directly line (the $x$-axis). The graph in $\textbf{Fig. P2.61}$ shows this animal'due south velocity every bit a role of fourth dimension. During the commencement 12.0 s, detect (a) the total altitude moved and (b) the displacement of the gazelle. (c) Sketch an $a_x-t$ graph showing this gazelle's acceleration as a function of fourth dimension for the starting time 12.0 s.
Ryan H.
Numerade Educator
Trouble 62
The engineer of a passenger train traveling at 25.0 1000/s sights a freight train whose caboose is 200 m ahead on the same track ($\textbf{Fig. P2.62}$). The freight train is traveling at 15.0 m/south in the same management equally the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant acceleration of 0.100 yard/due south$^ii$ in a direction opposite to the train'south velocity, while the freight train continues with constant speed. Take $ten =$ 0 at the location of the front of the passenger train when the engineer applies the brakes. (a) Will the cows nearby witness a collision? (b) If then, where volition it take identify? (c) On a single graph, sketch the positions of the front of the passenger train and the dorsum of the freight train.
Johnny K.
University of Minnesota - Twin Cities
Problem 63
A ball starts from remainder and rolls down a hill with compatible acceleration, traveling 200 yard during the second 5.0 south of its motion. How far did it whorl during the first five.0 south of motility?
Ryan H.
Numerade Educator
Problem 64
Ii cars commencement 200 m apart and drive toward each other at a steady 10 m/due south. On the front of one of them, an energetic grasshopper jumps back and forth between the cars (he has strong legs!) with a constant horizontal velocity of 15 yard/s relative to the footing. The insect jumps the instant he lands, so he spends no time resting on either car. What total distance does the grasshopper travel before the cars hit?
Johnny Yard.
University of Minnesota - Twin Cities
Problem 65
A motorcar and a truck offset from residual at the same instant, with the automobile initially at some distance behind the truck. The truck has a constant acceleration of 2.x g/s$^ii$, and the car has an acceleration of 3.40 m/s$^2$. The car overtakes the truck later on the truck has moved 60.0 m. (a) How much time does it take the car to overtake the truck? (b) How far was the car behind the truck initially? (c) What is the speed of each when they are abreast? (d) On a single graph, sketch the position of each vehicle equally a function of time. Have $x =$ 0 at the initial location of the truck.
Ryan H.
Numerade Educator
Problem 66
You are standing at rest at a bus cease. A bus moving at a constant speed of $5.00 \mathrm{~m} / \mathrm{~s}$ passes yous. When the rear of the omnibus is $12.0 \mathrm{~g}$ past you lot, you lot realize that it is your bus, so you start to run toward information technology with a constant acceleration of $0.960 \mathrm{~chiliad} / \mathrm{~s}^{2}$. How far would you accept to run before yous catch up with the rear of the bus, and how fast must you be running then? Would an average higher student be physically able to reach this?
Johnny G.
Academy of Minnesota - Twin Cities
Problem 67
The driver of a auto wishes to pass a truck that is traveling at a constant speed of 20.0 m/s (virtually 45 mi/h). Initially, the motorcar is also traveling at 20.0 chiliad/s, and its front bumper is 24.0 thousand behind the truck's rear bumper. The car accelerates at a constant 0.600 g/s$^ii$, then pulls back into the truck'south lane when the rear of the car is 26.0 yard alee of the front end of the truck. The car is 4.5 m long, and the truck is 21.0 m long. (a) How much fourth dimension is required for the car to laissez passer the truck? (b) What altitude does the car travel during this fourth dimension? (c) What is the final speed of the motorcar?
Ryan H.
Numerade Educator
Problem 68
An object'southward velocity is measured to be $v_x(t) =\alpha - \beta{t}^2$, where $\blastoff$ = 4.00 m/south and $\beta$ = two.00 m/s$^3$. At $t =$ 0 the object is at $ten =$ 0. (a) Calculate the object's position and dispatch as functions of time. (b) What is the object'southward maximum $positive$ displacement from the origin?
Johnny G.
Academy of Minnesota - Twin Cities
Problem 69
The dispatch of a particle is given past $a_x(t) =$ -2.00 m/southward$^2$ + 13.00 yard/s$^three)t$. (a) Find the initial velocity $v_{0x}$ such that the particle will have the same $x$-coordinate at $t =$ four.00 s every bit it had at $t =$ 0. (b) What volition be the velocity at $t =$ iv.00 s?
Ryan H.
Numerade Educator
Problem 70
Y'all are on the roof of the physics building, 46.0 m above the ground ($\textbf{Fig. P2.lxx}$). Your physics professor, who is i.80 m tall, is walking alongside the building at a constant speed of 1.20 m/s. If you lot wish to drop an egg on your professor'south head, where should the professor exist when y'all release the egg? Presume that the egg is in gratis autumn.
Johnny G.
University of Minnesota - Twin Cities
Trouble 71
A certain volcano on earth can eject rocks vertically to a maximum height $H$. (a) How high (in terms of $H$) would these rocks go if a volcano on Mars ejected them with the same initial velocity? The acceleration due to gravity on Mars is 3.71 thousand/south$^2$; ignore air resistance on both planets. (b) If the rocks are in the air for a fourth dimension $T$ on earth, for how long (in terms of $T$) would they be in the air on Mars?
Ryan H.
Numerade Educator
Problem 72
An entertainer juggles balls while doing other activities. In one act, she throws a brawl vertically upward, and while information technology is in the air, she runs to and from a tabular array five.50 one thousand away at an boilerplate speed of 3.00 m/due south, returning but in time to take hold of the falling brawl. (a) With what minimum initial speed must she throw the ball upward to reach this feat? (b) How loftier above its initial position is the ball simply as she reaches the table?
Johnny G.
University of Minnesota - Twin Cities
Problem 73
Sam heaves a 16-lb shot straight upward, giving it a abiding up acceleration from residue of 35.0 thousand/s$^2$ for 64.0 cm. He releases information technology 2.20 m above the ground. Ignore air resistance. (a) What is the speed of the shot when Sam releases it? (b) How loftier higher up the ground does it get? (c) How much time does he have to leave of its way earlier it returns to the height of the height of his head, i.83 one thousand above the ground?
Ryan H.
Numerade Educator
Problem 74
A flowerpot falls off a windowsill and passes the window of the story below. Ignore air resistance. It takes the pot 0.380 s to pass from the top to the bottom of this window, which is i.90 m loftier. How far is the superlative of the window below the windowsill from which the flowerpot fell?
Johnny G.
University of Minnesota - Twin Cities
Trouble 75
Two stones are thrown vertically up from the footing, one with 3 times the initial speed of the other. (a) If the faster rock takes x s to return to the ground, how long will it take the slower rock to return? (b) If the slower stone reaches a maximum height of $H$, how high (in terms of $H$) volition the faster stone go? Presume free fall.
Ryan H.
Numerade Educator
Problem 76
In the commencement phase of a 2-phase rocket, the rocket is fired from the launch pad starting from rest but with a constant acceleration of 3.50 yard/south$^2$ upward. At 25.0 s later on launch, the 2nd stage fires for 10.0 s, which boosts the rocket'southward velocity to 132.5 chiliad/s upwards at 35.0 south later launch. This firing uses upward all of the fuel, however, so afterwards the second stage has finished firing, the only force acting on the rocket is gravity. Ignore air resistance. (a) Find the maximum superlative that the stage-two rocket reaches higher up the launch pad. (b) How much time later on the cease of the stage-ii firing will it accept for the rocket to fall back to the launch pad? (c) How fast will the stage-ii rocket be moving just as it reaches the launch pad?
Johnny Grand.
University of Minnesota - Twin Cities
Trouble 77
During your summer internship for an aerospace company, y'all are asked to pattern a small enquiry rocket. The rocket is to be launched from rest from the earth's surface and is to achieve a maximum height of 960 thou above the earth's surface. The rocket'southward engines give the rocket an upwards dispatch of 16.0 m/due south$^2$ during the time $T$ that they fire. After the engines close off, the rocket is in gratuitous fall. Ignore air resistance. What must be the value of $T$ in social club for the rocket to reach the required altitude?
Ryan H.
Numerade Educator
Trouble 78
A physics instructor performing an outdoor demonstration of a sudden falls from rest off a high cliff and simultaneously shouts "Aid." When she has fallen for 3.0 southward, she hears the echo of her shout from the valley floor below. The speed of sound is 340 yard/s. (a) How alpine is the cliff? (b) If we ignore air resistance, how fast will she be moving just before she hits the ground? (Her bodily speed will be less than this, due to air resistance.)
Johnny G.
University of Minnesota - Twin Cities
Problem 79
A helicopter conveying Dr. Evil takes off with a constant upwards acceleration of 5.0 m/south$^ii$. Surreptitious agent Austin Powers jumps on but equally the helicopter lifts off the ground. After the ii men struggle for 10.0 south, Powers shuts off the engine and steps out of the helicopter. Assume that the helicopter is in free fall after its engine is shut off, and ignore the furnishings of air resistance. (a) What is the maximum elevation above ground reached by the helicopter? (b) Powers deploys a jet pack strapped on his dorsum 7.0 southward after leaving the helicopter, and then he has a constant downwards acceleration with magnitude 2.0 m/s$^2$. How far is Powers above the ground when the helicopter crashes into the ground?
Ryan H.
Numerade Educator
Problem 80
You are climbing in the High Sierra when you suddenly find yourself at the edge of a fog-shrouded cliff. To notice the meridian of this cliff, you drop a rock from the top; 8.00 s later on you hear the sound of the rock hitting the footing at the foot of the cliff. (a) If you ignore air resistance, how high is the cliff if the speed of audio is 330 grand/s? (b) Suppose yous had ignored the time it takes the audio to reach y'all. In that case, would y'all take overestimated or underestimated the height of the cliff? Explain.
Johnny G.
Academy of Minnesota - Twin Cities
Problem 81
An object is moving along the $ten$-centrality. At $t =$ 0 it has velocity $v_{0x}$ = 20.0 grand/s. Starting at time $t =$ 0 it has acceleration $a_x = -Ct$, where $C$ has units of yard/southward$^three$. (a) What is the value of $C$ if the object stops in eight.00 s after $t =$ 0? (b) For the value of $C$ calculated in function (a), how far does the object travel during the 8.00 s?
Ryan H.
Numerade Educator
Problem 82
A brawl is thrown directly upwardly from the basis with speed $v_0$. At the same instant, a second ball is dropped from residue from a height $H$, directly above the betoken where the outset brawl was thrown upward. In that location is no air resistance. (a) Find the fourth dimension at which the two assurance collide. (b) Find the value of $H$ in terms of $v_0$ and $yard$ such that at the instant when the assurance collide, the offset ball is at the highest point of its motion.
Johnny One thousand.
University of Minnesota - Twin Cities
Trouble 83
Cars $A$ and $B$ travel in a direct line. The distance of $A$ from the starting point is given as a function of time by $x_A(t) = \alpha{t} + \beta{t}^2$, with $\alpha =$ 2.60 m/south and $\beta =$ 1.20 m/s$^2$. The distance of $B$ from the starting point is $x_B(t) = \gamma{t}^2 - \delta{t}^iii$, with $\gamma =$ ii.80 thou/south$^2$ and $\delta =$ 0.twenty chiliad/s$^three$. (a) Which car is ahead only after the ii cars leave the starting point? (b) At what fourth dimension(s) are the cars at the aforementioned signal? (c) At what time(s) is the altitude from $A$ to $B$ neither increasing nor decreasing? (d) At what time(s) practise $A$ and $B$ accept the same acceleration?
Ryan H.
Numerade Educator
Problem 84
In your physics lab you release a small glider from residual at various points on a long, frictionless air track that is inclined at an angle $\theta$ above the horizontal. With an electronic photocell, you lot measure out the time $t$ it takes the glider to slide a distance $ten$ from the release point to the lesser of the track. Your measurements are given in $\textbf{Fig. P2.84}$, which shows a 2d-order polynomial (quadratic) fit to the plotted data. You are asked to observe the glider'due south acceleration, which is assumed to be constant. There is some error in each measurement, so instead of using a single set of $x$ and $t$ values, you can be more than accurate if you use graphical methods and obtain your measured value of the acceleration from the graph. (a) How tin you re-graph the data so that the information points fall shut to a straight line? ($Hint:$ Yous might want to plot $10$ or $t$, or both, raised to some power.) (b) Construct the graph you described in function (a) and find the equation for the straight line that is the best fit to the data points. (c) Use the straightline fit from part (b) to calculate the acceleration of the glider. (d) The glider is released at a distance $10 =$ 1.35 m from the bottom of the track. Use the acceleration value yous obtained in role (c) to calculate the speed of the glider when it reaches the lesser of the track.
Johnny Thousand.
University of Minnesota - Twin Cities
Problem 85
In a physics lab experiment, you lot release a small steel brawl at various heights above the ground and measure the ball'southward speed simply before information technology strikes the ground. You plot your information on a graph that has the release acme (in meters) on the vertical axis and the square of the final speed (in m$^2$/s$^2$) on the horizontal axis. In this graph your data points lie close to a straight line. (a) Using $g$ = 9.80 1000/due south$^2$ and ignoring the effect of air resistance, what is the numerical value of the slope of this straight line? (Include the right units.) The presence of air resistance reduces the magnitude of the downwardly acceleration, and the event of air resistance increases as the speed of the object increases. You repeat the experiment, merely this time with a tennis ball every bit the object existence dropped. Air resistance at present has a noticeable issue on the data. (b) Is the final speed for a given release height higher than, lower than, or the aforementioned equally when yous ignored air resistance? (c) Is the graph of the release acme versus the square of the final speed still a straight line? Sketch the qualitative shape of the graph when air resistance is nowadays.
Ryan H.
Numerade Educator
Trouble 86
A model car starts from rest and travels in a straight line. A smartphone mounted on the car has an app that transmits the magnitude of the car's acceleration (measured by an accelerometer) every 2nd. The results are given in the table:
Each measured value has some experimental error. (a) Plot acceleration versus time and find the equation for the direct line that gives the best fit to the information. (b) Employ the equation for $a(t)$ that you constitute in part (a) to calculate $v(t)$, the speed of the motorcar equally a function of fourth dimension. Sketch the graph of $v$ versus $t$. Is this graph a straight line? (c) Employ your upshot from office (b) to calculate the speed of the car at $t =$ 5.00 s. (d) Calculate the distance the car travels between $t =$ 0 and $t =$ 5.00 s.
Johnny M.
Academy of Minnesota - Twin Cities
Trouble 87
In the vertical jump, an athlete starts from a crouch and jumps upwardly every bit high equally possible. Even the all-time athletes spend fiddling more 1.00 s in the air (their "hang time"). Care for the athlete every bit a particle and let $y_{max}$ exist his maximum pinnacle to a higher place the flooring. To explicate why he seems to hang in the air, calculate the ratio of the time he is to a higher place $y_{max}$/2 to the time it takes him to go from the flooring to that height. Ignore air resistance
Suzanne W.
Numerade Educator
Problem 88
A student is running at her acme speed of 5.0 k/s to grab a bus, which is stopped at the motorcoach stop. When the pupil is still 40.0 1000 from the bus, it starts to pull away, moving with a constant acceleration of 0.170 thou/s$^2$. (a) For how much time and what distance does the student have to run at five.0 m/s earlier she overtakes the double-decker? (b) When she reaches the autobus, how fast is the jitney traveling? (c) Sketch an $x-t$ graph for both the student and the double-decker. Accept $10 =$ 0 at the initial position of the student. (d) The equations you used in part (a) to observe the time have a 2nd solution, corresponding to a later time for which the student and autobus are once again at the aforementioned place if they continue their specified motions. Explain the significance of this second solution. How fast is the bus traveling at this point? (due east) If the student's top speed is iii.5 grand/south, will she catch the bus? (f) What is the $minimum$ speed the student must accept to but take hold of upward with the passenger vehicle? For what time and what distance does she have to run in that example?
Johnny 1000.
Academy of Minnesota - Twin Cities
Trouble 89
A ball is thrown straight up from the border of the roof of a building. A second ball is dropped from the roof i.00 s afterwards. Ignore air resistance. (a) If the peak of the building is 20.0 k, what must the initial speed of the beginning ball be if both are to hit the ground at the same fourth dimension? On the same graph, sketch the positions of both balls as a function of time, measured from when the starting time ball is thrown. Consider the same state of affairs, only now let the initial speed $v_0$ of the commencement ball exist given and treat the height $h$ of the building as an unknown. (b) What must the height of the building be for both balls to reach the ground at the same time if (i) $v_0$ is six.0 m/south and (two) $v_0$ is ix.v one thousand/s? (c) If $v_0$ is greater than some value $v_{max}$, no value of h exists that allows both assurance to hitting the footing at the same time. Solve for $v_{max}$. The value $v_{max}$ has a unproblematic physical interpretation. What is it? (d) If $v_0$ is less than some value $v_{min}$, no value of h exists that allows both balls to hit the basis at the aforementioned time. Solve for $v_{min}$. The value $v_{min}$ also has a simple physical interpretation. What is information technology?
Ryan H.
Numerade Educator
Problem 90
If the wrinkle of the left ventricle lasts 250 ms and the speed of blood flow in the aorta (the large avenue leaving the heart) is 0.80 1000/s at the end of the contraction, what is the average dispatch of a red blood cell as information technology leaves the heart? (a) 310 ms$^2$; (b) 31 k/s$^two$; (c) iii.2 yard/s$^2$; (d) 0.32 m/s$^2$.
Johnny G.
University of Minnesota - Twin Cities
Problem 91
If the aorta (diameter $d_a$) branches into two equal-sized arteries with a combined area equal to that of the aorta, what is the diameter of one of the branches? (a) $\sqrt{d_a}$; (b) $d_a/\sqrt{2}$; (c) 2$d_a$; (d) $d_a/2$.
Ryan H.
Numerade Educator
Trouble 92
The velocity of blood in the aorta can be measured directly with ultrasound techniques. A typical graph of claret velocity versus fourth dimension during a single heartbeat is shown in $\textbf{Fig. P2.92.}$ Which argument is the all-time interpretation of this graph? (a) The blood period changes direction at about 0.25 s; (b) the speed of the blood period begins to subtract at about 0.10 s; (c) the acceleration of the blood is greatest in magnitude at nearly 0.25 s; (d) the dispatch of the blood is greatest in magnitude at near 0.ten southward.
Johnny G.
University of Minnesota - Twin Cities
Source: https://www.numerade.com/books/chapter/motion-along-a-straight-line/
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