Solution: A rock is thrown (not dropped) straight down from

A person gets in an elevator on the ground floor and rides it to the top floor of a building. Sketch a velocity-versus-time graph for this motion.

a. Give an example of a vert.ical motion with a positive velocity and a negative acceleration. b. Give an example of a vertical motion with a negative velocity and a negative acceleration.

Figure Q2.3 shows growth rings in the trunk of a pine tree. BIO You can clearly see the wide and the narrow rings that correspond to years of fast and slow growth. You can think of these rings as a motion diagram for the growth of the tree. If we define an axis as shown, with x measured out from the center of the tree, use the appearance of the rings to sketch a velocity- versus-time graph for the radial growth of the tree.

Sketch a velocity-versus-time graph for a rock that is thrown straight upward, from the instant it leaves the hand until the instant it hits the ground.

You are driving down the road at a constant speed. Another car going a bit faster catches up with you and passes you. Draw a position graph for both vehicles on the same set of axes, and note the point on the graph where the other vehicle passes you.

A car is traveling nonh. Can its acceleration vector ever point south? Explain.

Certain animals are capable of running at great speeds; other BIO animals are capable of tremendous accelerations. Speculate on which would be more beneficial to a predator- large maximum speed or large acceleration.

A ball is thrown straight up into the air. At each of the fo llowing instants, is the ball's acceleration a_. equal tog, - g, 0, < g, or >g? a. Just after leaving your hand? b. At the very top (maximum height)? c. Just before hitting the ground?

A rock is thrown (not dropped) straight down from a bridge into the river below. a. Immediately after being released, is the magnitude of the rock's acceleration greater than g, less than g, or equal to g? Explain. b. Immediately before hitting the water, is the magnitude of the the rock's acceleration greater than g, less than g, or equal tog? Explain.

Figure Q2. IO shows an object's position-versus-time graph. The letters A to E correspond to various segments of the motion in which the graph has constant slope. a. Write a realistic motion short story for an object that would have this posit.ion graph. b. In which segment(s) is the object at rest? c. In which segment(s) is the object moving to the right? d. Is the speed of the object during segment C greater than, equal to, or less than its speed during segment E? Explain.

Figure Q2. l I shows the position graph for an object moving along the horizontal axis. a. Write a realistic motion short story (or an object that would have this position graph. b. Draw the corresponding velocity graph.

Figure Q2.12 shows the position-versus-time graphs for two objects, A and B, that are moving along the same axi s. a. At the instant t = I s, is the speed of A greater than, less than, or equal to the speed of B? Explain. b. Do objects A and Bever have the same speed? If so, at what time or times? Explain.

Figure Q2.12 shows the position-versus-time graphs for two objects, A and B, that are moving along the same axi s. a. At the instant t = I s, is the speed of A greater than, less than, or equal to the speed of B? Explain. b. Do objects A and Bever have the same speed? If so, at what time or times? Explain.

Figure Q2.14 is the velocity-versus-time graph for an object moving along the x-axis. a. During which segment(s) is the velocity constant? b. During which segment(s) is the object speeding up? c. During which segment(s) is the object slowing down? d. During which segment(s) is the object standing still? e. During which segment(s) is the object moving to the right?

Figure Q2.15 shows the position graph of a car traveling on a straight road. At which labeled instant is the speed of the car greatest?

Figure Q2. l 6 shows the position graph of a car traveling on a straight road. The velocity at instant 1 is ____ and the velocity at instant 2 is ___ _ A. positive, negative B. positive, positive C. negative, negative D. negative, zero E. positive, zero

Figure Q2. l 7 shows an object's position-versus-time 20 graph. What is the velocity of 10 the object at t = 6 s? A. 0.67 mis B. 0.83 mis C. 3.3 mis E. 25 mis

The fo llowing options describe the motion of four cars A-D. Which car has the largest acceleration? A. Goes from 0 mis to 10 mis in 5.0 s B. Goes from 0 mis to 5.0 mis in 2.0 s C. Goes from 0 mis to 20 mis in 7.0 s D. Goes from 0 mis to 3.0 mis in 1.0 s

A car is traveling at vx = 20 mis. The driver applies the brakes, and the car slows with ax= - 4.0 mls2 What is the stopping distance? A. 5.0 m B. 25 m C. 40 m D. 50 m

Velocity-versus-time graphs for three drag racers are shown in Figure Q2.20. At t = 5.0 s, which car has traveled the farthest? A. Andy B. Betty C. Carl D. All have traveled the same distance

Which of the three drag racers in Question 20 had the greatest acceleration at t = 0 s? A. Andy B. Betty C. Carl D. All had the same acceleration

Chris is holding two softballs while s tanding on a balcony. She throws ball 1 straight up in the air and, at the same instant, releases her gri p on ball 2, letting it drop over the side of the building. Which velocity graph in Figure Q2.22 best represents the motion of the two balls?

Suppose a plane accelerates from rest for 30 s, achieving a takeoff speed of 80 mis after traveling a distance of 1200 m down the runway. A smaller plane with the same acceleration has a takeoff speed of 40 mis. Starting from rest, after what distance will th is smaller plane reach its takeoff speed? A. 300 m 13. 600 m C. 900 m D. 1200 m

Figure Q2.24 shows a motion diagram with the clock reading (in seconds) shown at each position. From t = 9 s to t = 15 s the object is at the same position. After that, it returns along the same track. The positions of the dots for t ~ 16 s are offse t for clarity. Which graph best represents the object's velocity?

A car can go from 0 to 60 mph in 7.0 s. Assuming that it could maintain the same acceleration at higher speeds, how long would it take the car to go from 0 to 120 mph? A. IOs B. 14 s C.21 s D. 28 s

A car can go from 0 to 60 mph in 12 s. A second car is capable of twice the acceleration of the first car. Assuming that it could maintain the same acceleration at higher speeds, how much time will this second car take to go from 0 to 120 mph? A. 12 s B. 9.0 s C. 6.0 s D. 3.0 s

a. What constant acceleration, in SI units, must a car have to go from zero to 60 mph in IO s? b. What fraction of g is this? c. How far has the car traveled when it reaches 60 mph? Give your answer both in ST units and in feet.

When j umping, a flea rapidly extends its legs, reaching a BKl takeoff speed of 1.0 mis over a distance of 0.50 mm. a. What is the flea's acceleration as it extends its legs? b. How long does it take the flea to leave the ground after it begins pushing off?

A car traveling at speed v takes distance d to stop after the brakes are applied. What is the stopping distance if the car is initially traveling at speed 2v? Assume that the acceleration due to the braking is the same in both cases.

Light-rail passenger trains that provide transportation within and between cities speed up and slow down with a nearly constant (and quite modest) acceleration. A train travels through a congested part of town at 5.0 mis. Once free of this area, it speeds up to 12 mis in 8.0 s. At the edge of town, the driver again accelerates, with the same acceleration, for another 16 s to reach a higher cruisi ng speed. What is the fi nal speed?

A cross-country skier is skiing along at a zippy 8.0 mis. She stops pushing and simply glides along, slowing to a reduced speed of 6.0 mis after gliding for 5.0 m. What is the magnitude of her acceleration as she slows?

A small propeller airplane can comfortably achieve a high enough speed to take off on a runway that is 1/4 mile long. A large, fully loaded passenger jet has about the same acceleration from rest, but it needs to achieve twice the speed to take off. What is the minimum runway length that wi ll serve? Hint: You can solve this problem using ratios without having any additional information

Formula One racers speed up much more quickly than normal passenger vehicles, and they also can stop in a much shorter distance. A Formula One racer traveling at 90 mis can stop in a distance of 110 m. What is the magnitude of the car's acceleration as it slows during braking?

igure P2.34 shows a velocity-versus-time graph for a particle moving along the x-axis. Al t = 0 s, assume that x = 0 m. a. What are the particle's position, velocity, and acceleration at I = 1.0 s? b. What are tbe particle's position, velocity, and acceleration at I = 3.0 s?

A driver has a reaction time of 0.50 s, and the maximum deceleration of her car is 6.0 m/s2. She is driving at 20 mis when suddenly she sees an obstacle in the road 50 m in front of her. How much time does it take Can she stop the car in time to avoid a collision?

Chameleons catch insects with their tongues, which they can 44. Ill In the preceding problem we saw that a person's reaction BIO rapidly extend to great lengths. In a typical strike, the chameleon's BIO time is generally nor quick enough to allow the person to catch tongue accele rates at a remarkable 250 m/s2 for 20 ms, then a $1 bill dropped between the fingers. The 16 cm length of the travels at constant speed for another 30 ms. During this total time bill passes through a student's fingers before she can grab it if of 50 ms, 1/20 of a second, how far does the tongue reach?

You' re driving down the highway late one night at 20 m/s when a deer steps onto the road 35 min front of you. Your reaction time before stepping on the brakes is 0.50 s, and the maximum deceleration of your car is 10 m/s2 a. How much distance is between you and the deer when yo come to a stop? b. What is the maximum speed you could have and still not hit the deer?

A light-rail train going from one station to the next on a magnistraight section of track accelerates from rest at I. I m/s2 for 20 s.lt then proceeds at constant speed for 1100 m before slowing down at 2.2 m/s2 until it stops at the station. a. What is the distance between the stations? b. How far is the motorcycle from the car when it reaches this speed?

A car is traveling at a steady 80 km/h in a 50 km/h zone. A police motorcycle takes off at the instant the car passes it, accelerating at a steady 8.0 m/s2. a. How much time elapses before the motorcycle is moving as fast as the car? How far is the motorcycle from the car when it reaches this speed?

When a jet lands on an aircraft carrier, a hook on the tail of the plane grabs a wire that quickly brings the plane to a halt before it overshoots the deck. a. What is the magni tude of the jet's acceleration as it is brought to rest? b. How much time does the landing take?

A simple model for a person running the I 00 m dash is to assume the sprinter runs with constant accele ration until reaching top speed, then maintai ns that speed through the fini sIf a sprinter reaches his top speed of 11.2 mis in 2. 14 s, what line. will be his total time?

Ball bearings can be made by letting spherical drops of molten metal fall inside a tall tower--called a shol tower- and solidify as they fall. a. If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be? b. What is the bearing's impact velocity?

Here's an interesting chalBIO lenge you can give to a friend. Hold a $I (or larger!) bill by an upper corner. Have a friend prepare to pinch a lower corner, putting her fingers near but not touching the bill. Tell her to try to catch the bill when you drop it by simply closing her fingers. This seems like it should be easy, but it's not. After she sees that you have released the bill, it will take her about 0.25 s to react and close her fingers- which is not fast enough to catch the bill. How much time does it take for the bill to fall beyond her grasp? The length of a bill is 16 cm.

In the preceding problem we saw that a person's reaction time is generally nor quick enough to allow the person to catch a $1 bill dropped between the fingers. The 16 cm length of the bill passes through a student's fingers before she can grab it if she has a typical 0.25 s reaction time. How long would a bill need to be for her to have a good chance of catching it?

A gannet is a seabird that fishes by diving from a great height. If a gannet hits the water at 32 mis (which they do), what height did it dive from? Assume that the gannet was motionless before starting its dive.

A student at the top of a building of height h throws ball A straight upward with speed v0 and throws ball B straight downward with the same initial speed. a. Compare the balls' accelerations, both direction and magnitude, immediately after they leave her hand. Is one accelerati on larger than the other? Or are the magnitudes equal? b. Compare the final speeds of the balls as they reach the ground. Is one larger than the other? Or are they equal?

Excellent human jumpers can leap straight up to a height of 110 cm off the ground. To reach this height, with what speed would a person need to leave the ground?

A football is kicked straight up into the air; it hits the ground 5.2 s later. a. What was the greatest height reached by the ball? Assume it is kicked from ground level. b. With what speed did it leave the kicker's foot?

In an action movie, the villain is rescued from the ocean by grabbing onto the ladder hanging from a helicopter. He is so intent on gripping the ladder that he lets go of his briefcase of counterfeit money when he is 130 m above the water. If the briefcase hits the water 6.0 s later, what was the speed at which the helicopter was ascending?

Spud Webb was, at 5 ft 8 in, one of the shortest basketball players to play in the NBA. But he had an amazing vertical leap; he could jump to a height of I. I m off the ground, so he could easily dunk a basketball. For such a leap, what was his "hang time"-the time spent in the air after leaving the ground and before touching down again?

A rock climber stands on top of a 50-m-high cliff overhanging a pool of water. He throws two stones vertically downward 1.0 s apart and observes that they cause a single splash. The initial speed of the first stone was 2.0 mis. a. How long after the release of the first stone does the second stone hit the water? b. What was the initial speed of the second stone? c. What is the speed of each stone as it hits the water?

Actual velocity data for a BIO lion pursuing prey are shown in Figure P2.52. Estimate: a. The initial acceleration of the lion. b. The acceleration of the lion at 2 s and at 4 s. c. The distance traveled by the lion between Os and 8 s.

A trnck driver has a shipment of apples to deliver to a destination 440 miles away. The trip usually takes him 8 hours. Today he finds himself daydreaming and realizes 120 miles into his trip that he is running 15 minutes later than his usual pace at this point. At what speed must he drive for the remainder of the trip to complete the trip in the usual amount of time?

When you sneeze, the air in your lungs accelerates from rest BIO to approximately 150 km/h in about 0.50 seconds. a. What is the acceleration of the air in m/s2? b. What is this acceleration, in units of g?

Figure P2.55 shows the motion diagram, made at two frames of film per second, of a ball rolling along a track. The track has a 3.0-m-long sticky section.FIGURE P2.55 a. Use the scale to determine the positions of the center of the ball. Place your data in a table, similar to Table 2. 1, showing each position and the instant of time at which it occurred. b. Make a graph of x versus t for the ball. Because you have data only at certain instants of time, your graph should consist of dots that are not connected together. c. What is the change in the ball's position from t = 0 s to I= I.O s? d. What is the change in the ball's position from t = 2.0 s to I = 4.0 s? e. What is the ball's velocity before reaching the sticky section? f. What is the ball's velocity after passing the sticky section? g. Determine the ball's acceleration on the sticky section of the track.

Julie drives 100 mi to Grandmother' s house. On the way to Grandmother' s, Julie drives half the distance at 40 mph and half the distance at 60 mph. On her return trip, she drives half the time at 40 mph and half the time at 60 mph. a. How long does it take Julie to complete the trip to Grandmother's house? b. How long does the return trip take?

The takeoff speed for an Airbus A320 I jetliner is 80 mis. Velocity data measured during takeoff are as shown in the table. a. What is the jetliner's acceleration during takeoff, in mls2 and in g's? b. At what time do the wheels leave the ground? c. For safety reasons, in case of an aborted takeoff, the length of the runway must be three ti mes the takeoff distance. What is the minimum length nmway this aircraft can use?

Does a real automobile have constant accelerat.ion? Measured data for a Porsche 944 Turbo at maximum acceleration are as shown in the table. a. Convert the velocities to mis, then make a graph of velocity versus time. Based on your graph, is the acceleration constant? Explain. b. Draw a smooth curve through the points on your graph, then use your graph to estimate the car's acceleration at 2.0 s and 8.0 s. Give your answer in SI units. Hint: Remember that acceleration is the slope of the velocity graph.

People hoping to travel to other worlds are faced with huge challenges. One of the biggest is the lime required for a joumey. The nearest star is 4.1 X 1016 m away. Suppose you had a spacecraft that could accelerate at l .Og for half a year, then continue at a constant speed. (This is far beyond what can be achieved with any known technology.) How long would it take you to reach the nearest star to earth?

You are driving to the grocery store at 20 mis. You are 110 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.70 s and that your car brakes with constant acceleration. a. How far are you from the intersection when you begin to apply the brakes? b. What acceleration wi ll bring you to rest right at the intersection? c. How long does it take you to stop?

When you blink your eye, the upper lid goes from rest with BlO your eye open to completely covering your eye in a time of 0.024 s. a. Estimate the distance that the top lid of your eye moves during a blink. b. What is the acceleration of your eyelid? Assume it to be constant. c. What is your upper eyelid' s final speed as it hits the bottom eyelid?

A bush baby, an African BlO primate, is capable of a remarkable vertical leap. The bush baby goes into a crouch and extends its legs, pushing upward for a distance of 0. 16 m. After this upward acceleration, the bush baby leaves the ground and travels upward for 2.3 m. What is the acceleration during the pushing-off phase? Give your answer in m/s2 and in g's.

When jumping, a flea reaches a takeoff speed of 1.0 mis over BIO a distance of 0.50 mm. a. What is the flea's acceleration during the jump phase? b. How long does the acceleration phase last? c. If the flea jumps straight up, how high will it go? (Ignore air resistance for this problem; in reality, air resistance plays a large role, and the flea will not reach this height.)

Certain insects can achieve -,ir-.lll'i:&::l!!I BIO seemingly impossible accelerations whi le jumpi_ng. The click beetle accelerates at an astonishing 400g over a distance of 0.60 cm as it rapidly bends its thorax, making the "click" that gives it its name. a. Assuming the beetle jumps straight up, at what speed does it leave the ground? b. How much time is required for the beetle to reach this speed? c. Ignoring air resistance, how high would it go?

A student standing on the ground throws a ball straight up. The ball leaves the student's hand with a speed of 15 mis when the hand is 2.0 m above the ground. How long is the ball in the air before it hits the ground? (The student moves her hand out of the way.)

A rock is tossed straight up wi th a speed of 20 mis. When it returns, it falls into a hole 10 m deep. a. What is the rock's velocity as it hits the bottom of the hole? b. How long is the rock in the air, from the instant it is released until it hits the bottom of the hole?

A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 30.0 mls2 for 30.0 s, then runs out of fuel. Ignore any air resistance effects. a. What is the rocket's maximum altitude? b. How long is the rocket in the air? c. Draw a velocity-versus-time graph for the rocket from liftoff until it hits the ground.

A hotel e levator ascends 200 m with a maximum speed of 5.0 mis. Its acceleration and deceleration both have a magnitude of 1.0 mls2 . a. How far does the elevator move while accelerating to full speed from rest? b. How long does it take to make the complete trip from bottom to top?

A car starts from rest at a stop sign. It accelerates at 2.0 mls2 for 6.0 seconds, coasts for 2.0 s, and then slows down at a rate of 1.5 mls2 for the next stop sign. How far apart are the stop signs?

A toy train is pushed forward and released at x; = 2.0 m with a speed of 2.0 mis. Tt rolls at a steady speed for 2.0 s, then one wheel begins to stick. The train comes to a stop 6.0 m from the point at which it was released. What is the train's acceleration after its wheel begins to stick?

Heather and Jerry are standing on a bridge 50 m above a river. Heather throws a rock straight down with a speed of 20 mis. Jen-y, at exactly the same instant of time, throws a rock straight up with the same speed. Ignore air resistance. a. How much time elapses between the first splash and the second splash? b. Which rock has the faster speed as it hi ts the water?

A Thomson's gazelle can run at very high speeds, but its BIO acceleration is relatively modest. A reasonable model for the sprint of a gazelle assumes an acceleration of 4.2 m/s2 for 6.5 s, after which the gazelle continues at a steady speed. a. What is the gazelle's top speed? b. A human would win a very short race with a gazelle. The best time for a 30 m sprint for a human runner is 3.6 s. How Much time would the gazelle take for a 30 m race? c. A gazelle would win a longer race. The best time for a 200 m sprint for a human runner is 19.3 s. How much time would the gazelle take for a 200 m race?

We've seen that a man's higher initial acceleration means that BIO a man can outrun a horse over a very sho1t race. A simple- but plausible-model for a sp1i nt by a man and a horse uses the following assumptions: The man acoelerates at 6.0 mls2 for 1.8 s and then runs at a constant speed. A horse accelerates at a more modest 5.0 mls2 but continues accelerating for 4.8 s and then continues at a constant speed. A man and a horse are competing in a 200 m race. The man is given a I 00 m head start, so he begins I 00 m from the finish line. How much time does the man take to complete the race? How much time does the horse take? Who wins the race?

A pole-vaulter is nearly motionless as he clears the bar, set 4.2 m above the ground. He then falls onto a thick pad. The top of the pad is 80 cm above the ground, and it compresses by 50 cm as he comes to rest. What is his acceleration as he comes to rest on the pad?

A Porsche challenges a Honda to a 400 m race. Because the Porsche's acceleratiou of 3.5 mls2 is larger than the Honda's 3.0 mls2, the Honda gets a 100-m head start- it is only 300 m from the fini sh line. Assume, somewhat unrealistically, that both cars can maintain these accelerations the entire distance. Who wi ns, and by how much time?

The minimum stopping distance for a car traveling at a speed of 30 mis is 60 m, including the distance traveled during the driver's reaction time of 0.50 s. a. Draw a position-versus-time graph for the motion of the car. Assume the car is at x; = 0 111 when the driver first sees the emergency situation ahead that calls for a rapid halt. b. What is the minimum stoppi ng distance for the same car traveling at a speed of 40 mis?

A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.0 s later. What was the rocket's acceleration?

If an astronaut can jump straight up to a height of 0.50 m on earth, how high could he jump on the moon? A. l.2m B. 3.0m C. 3.6m D. 18m

On the earth, an astronaut can safely jump to the ground from a height of 1.0 m; her velocity when reaching the ground is slow enough to not cause injury. From what height could the astronaut safely jump to the ground on the moon? A. 2.4 m B. 6.0 m C. 7.2 m D. 36 m

On the earth, an astronaut throws a ball straight upward; it stays in the air for a total time of 3.0 s before reaching the ground again. If a ball were to be thrown upward with the same initial speed on the moon, how much time would pass before it hit the ground? A. 7.3 s B. 18 s C. 44 s D. 108 s