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physics
mechanics

College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions

Car A is in a straight- line distance d from a starting line, and Car B is a distance of 2 d from the line. Accelerating uniformly from rest, it is desired that both cars cross the starting line at the same speed. If so, which car has the greater acceleration, and how much greater?
How many variables must be known to solve a kinematic equation?
If the instantaneous velocity of an object is zero, is the acceleration necessarily zero?
A person drops a stone from the window of a building. One second later, she drops another stone. How does the distance between the stones vary with time?
How would free fall on the Moon differ from that on the Earth?
If the displacement of an object is 300 m north, what can you say about the distance traveled by the object?
A car is traveling at a constant speed of on a circular track. Is the car accelerating? Explain.
What is the magnitude of the displacement of a car that travels half a lap along a circle that has a radius of 150 m? How about when the car travels a full lap?
A race car travels a complete lap on a circular track of radius 500 m in 50 s. (a) The average velocity of the race car is (1) zero, (2) 100 m/s, (3) 200 m/s, (4) none of the preceding. Why? (b) What is the average speed of the race car?
A student runs 30 m east, 40 m north, and 50 m west. (a) The magnitude of the student’s net displacement is (1) between 0 and 20 m, (2) between 20 m and 40 m, (3) between 40 m and 60 m. (b) What is his net displacement?
A student throws a ball vertically upward such that it travels 7.1 m to its maximum height. If the ball is caught at the initial height 2.4 s after being thrown, (a) What is the ball’s average speed, and (b) What is its average velocity?
An insect crawls along the edge of a rectangular swimming pool of length 27 m and width 21 m (Fig. 2.19). If it crawls from corner A to corner B in 30 min,(a) What is its average speed, and (b) What is the magnitude of its average velocity?
A plot of position versus time is shown in Fig. 2.20 for an object in linear motion.(a) What are the average velocities for the segments AB, BC, CD, DE, EF, FG, and BG? (b) State whether the motion is uniform or nonuniform in each case. (c) What is the instantaneous velocity at point D?
In demonstrating a dance step, a person moves in one dimension, as shown in Fig. 2.21. What are(a) The average speed and (b) The average velocity for each phase of the motion? (c) What are the instantaneous velocities at t = 1.0 s, 2.5 s, 4.5 s, and 6.0 s? (d) What is the average velocity for
A high school kicker makes a 30.0-yd field goal attempt (in American football) and hits the crossbar at a height of 10.0 ft. (a) What is the net displacement of the football from the time it leaves the ground until it hits the crossbar? (b) Assuming the football took 2.50 s to hit the crossbar,
The location of a moving particle at a particular time is given by x = at – bt2, where and a = 10 m/s and b = 0.50 m/s2. (a) Where is the particle at t = 0? (b) What is the particle’s displacement for the time interval t1 = 2.0s and t2 = 4.0s?
The displacement of an object is given as a function of time by x = 3t2 m. What is the magnitude of the average velocity for (a) ∆t = 2.0 s – 0s, and (b) ∆t = 4.0 s – 2.0s?
Short hair grows at a rate of about 2.0 cm/month. A college student has his hair cut to a length of 1.5 cm. He will have it cut again when the length is 3.5 cm. How long will it be until his next trip to the barber shop?
A motorist travels 80 km at 100 km/h, and 50 km at 75 km/h. What is the average speed for the trip?
A student driving home for the holidays starts at 8: 00 AM to make the 675-km trip, practically all of which is on nonurban interstate highways. If she wants to arrive home no later than 3: 00 PM, what must be her minimum average speed? Will she have to exceed the speed limit?
A regional airline flight consists of two legs with an intermediate stop. The airplane flies 400 km due north from airport A to airport B. From there, it flies 300 km due east to its final destination at airport C. (a) What is the plane’s displacement from its starting point? (b) If the first
Two runners approaching each other on a straight track have constant speeds of 4.50 m/s and 3.50 m/s, respectively, when they are 100 m apart (Fig. 2.22).How long will it take for the runners to meet, and at what position will they meet if they maintain these speeds?
An automobile traveling at 15.0 km/h along a straight, level road accelerates to 65.0 km/h in 6.00 s. What is the magnitude of the auto’s average acceleration?
A sports car can accelerate from 0 to in 3.9 s. What is the magnitude of the average acceleration of the car in meters per second squared?
A couple is traveling by car down a straight high-way at 40 km/h. They see an accident in the distance, so the driver applies the brakes, and in 5.0 s the car uniformly slows down to rest. (a) The direction of the acceleration vector is (1) in the same direction as, (2) opposite to, (3) at
A paramedic drives an ambulance at a constant speed of on a straight street for ten city blocks. Because of heavy traffic, the driver slows to in 6.0 s and travels two more blocks. What was the average acceleration of the vehicle?
During liftoff, a hot-air balloon accelerates upward at a rate of 3.0 m/s2. The balloonist drops an object over the side of the gondola when the speed is 15 m/s. (a) What is the object’s acceleration after it is released (relative to the ground)? (b) How long does it take to hit the ground?
Anew-car owner wants to show a friend how fast her sports car is. The friend gets in his car and drives down a straight, level highway at a constant speed of 60 km/h to a point where the sports car is waiting. As the friend’s car just passes, the sports car accelerates at a rate of 2.0 m/s2. (a)
An Olympic sprinter can run 100 yd in 9.0 s. At the same rate, how long would it take the sprinter to run 100 m?
After landing, a jetliner on a straight runway taxis to a stop at an average velocity of – 35.0 km/h. If the plane takes 7.00 s to come to rest, what are the plane’s initial velocity and acceleration?
A train on a straight, level track has an initial speed of 1.50 m/s2. A uniform acceleration of is applied while the train travels 200 m. (a) What is the speed of the train at the end of this distance? (b) How long did it take for the train to travel the 200 m?
A hockey puck sliding along the ice to the left hits the boards head-on with a speed of 35 m/s. As it reverses direction, it is in contact with the boards for 0.095 s, before rebounding at a slower speed of 11 m/s. Deter-mine the average acceleration the puck experienced while hitting the boards.
What is the acceleration for each graph segment in Fig. 2.23? Describe the motion of the object over the total time interval.
Figure 2.24 shows a plot of velocity versus time for an object in linear motion.(a) Compute the acceleration for each phase of motion. (b) Describe how the object moves during the last time segment.
A car initially traveling to the right at a steady speed of 25 m/s for 5.0 s applies its brakes and slows at a constant rate of 5.0 m/s2 for 3.0 s. It then continues traveling to the right at a steady but slower speed with no additional braking for another 6.0 s. (a) To help with the calculations,
A train normally travels at a uniform speed of 72 km/h on a long stretch of straight, level track. On a particular day, the train must make a 2.0-min stop at a station along this track. If the train decelerates at a uniform rate of 1.0 m/s2 and, after the stop, accelerates at a rate of 0.50 m/s2,
At a sports car rally, a car starting from rest accelerates uniformly at a rate of 9.0 m/s2 over a straight-line distance of 100 m. The time to beat in this event is 4.5 s. Does the driver beat this time? If not, what must the minimum acceleration be to do so?
A car accelerates from rest at a constant rate of 2.0 m/s2 for 5.0 s. (a) What is the speed of the car at the end of that time? (b) How far does the car travel in this time?
A car traveling at is to stop on a 35-m-long shoulder of the road. (a) What is the required magnitude of the minimum acceleration? (b) How much time will elapse during this minimum deceleration until the car stops?
A senior citizen walks 0.30 km in 10 min, going around a shopping mall. (a) What is her average speed in meters per second? (b) If she wants to increase her average speed by 20 % when walking a second lap, what would her travel time in minutes have to be?
A motorboat traveling on a straight course slows uniformly from 60 km/h to 40 km/h in a distance of 50 m. What is the boat’s acceleration?
The driver of a pickup truck going 100 km/h applies the brakes, giving the truck a uniform deceleration of while it travels 20.0 m. (a) What is the speed of the truck in kilometers per hour at the end of this distance? (b) How much time has elapsed?
A roller coaster car traveling at a constant speed of 20.0 m/s on a level track comes to a straight incline with a constant slope. While going up the incline, the car has a constant acceleration of 0.750 m/s2 in magnitude. (a) What is the speed of the car at 10.0 s on the incline? (b) How far has
A rocket car is traveling at a constant speed of 250 km/h on a salt flat. The driver gives the car a reverse thrust, and the car experiences a continuous and constant deceleration of 8.25 m/s2. How much time elapses until the car is 175 m from the point where the reverse thrust is applied? Describe
Two identical cars capable of accelerating at 3.00 m/s2 are racing on a straight track with running starts. Car A has an initial speed of 2.50 m/s; car B starts with speed of 5.00 m/s. (a) What is the separation of the two cars after 10 s? (b) Which car is moving faster after 10 s?
According to Newton’s laws of motion (which will be studied in Chapter 4), a frictionless incline should provide an acceleration of down the incline. A student with a stopwatch finds that an object, starting from rest, slides down a 15.00-m very smooth incline in exactly 3.00 s. Is the incline
An object moves in the + x-direction at a speed of 40 m/s. As it passes through the origin, it starts to experience a constant acceleration of 3.5 m/s2 in the – x-direction. (a) What will happen next? (1) The object will reverse its direction of travel at the origin; (2) the object will keep
A rifle bullet with a muzzle speed of 330 m/s is fired directly into a special dense material that stops the bullet in 25.0 cm. Assuming the bullet’s deceleration to be constant, what is its magnitude?
The speed limit in a school zone is 40 km/h (about 25 mi/h). A driver traveling at this speed sees a child run onto the road 13 m ahead of his car. He applies the brakes, and the car decelerates at a uniform rate of 8.0 m/s2. If the driver’s reaction time is 0.25 s, will the car stop before
Assuming a reaction time of 0.50 s for the driver in Exercise 48, will the car stop before hitting the child?
A hospital patient is given 500 cc of saline by IV. If the saline is received at a rate of 4.0 mL/min, how long will it take for the half liter to run out?
A bullet traveling horizontally at a speed of 350 m/s hits a board perpendicular to its surface passes through and emerges on the other side at a speed of 210 m/s. If the board is 4.00 cm thick, how long does the bullet take to pass through it?
(a) Show that the area under the curve of a velocity-versus-time plot for a constant acceleration is equal to the displacement.(b) Compute the distance traveled for the motion represented by Fig. 2.23.
An object initially at rest experiences an acceleration of on a level surface. Under these conditions, it travels 6.00 m. Let’s designate the first 3.00 m as phase 1 with a subscript of 1 for those quantities, and the second 3.00 m as phase 2 with a subscript of 2. (a) The times for traveling
A car initially at rest experiences loss of its parking brake and rolls down a straight hill with a constant acceleration of 0.850 m/s2 traveling a total of 100 m. Let’s designate the first half of the distance as phase 1 with a subscript of 1 for those quantities, and the second half as phase 2
An object initially at rest experiences an acceleration of 1.5 m/s2 for 6.0 s and then travels at that constant velocity for another 8.0 s. What is the object’s average velocity over the 14-s interval?
Figure 2.24 shows a plot of velocity versus time for an object in linear motion.(a) What are the instantaneous velocities at t = 8.0 s and t = 11.0 s? (b) Compute the final displacement of the object. (c) Compute the total distance the object travels.
(a) A car traveling at a speed of v can brake to an emergency stop in a distance x. Assuming all other driving conditions are similar, if the traveling speed of the car doubles, the stopping distance will be (1) √2x, (2) 2x, (3) 4x. (b) A driver traveling at in a school zone can brake to an
A car accelerates horizontally from rest on a level road at a constant acceleration of 3.00 m/s2. Down the road, it passes through two photocells (“electric eyes” designated by 1 for the first one and 2 for the second one) that are separated by 20.0 m. The time interval to travel this 20.0-m
An automobile is traveling on a long, straight high-way at a steady 75.0 mi/h when the driver sees a wreck 150 m ahead. At that instant, she applies the brakes (ignore reaction time). Between her and the wreck are two different surfaces. First there is 100 m of ice, where the deceleration is only
A student drops a ball from the top of a tall building; the ball takes 2.8 s to reach the ground. (a) What was the ball’s speed just before hitting the ground? (b) What is the height of the building?
A hospital nurse walks 25 m to a patient’s room at the end of the hall in 0.50 min. She talks with the patient for 4.0 min, and then walks back to the nursing station at the same rate she came. What was the nurse’s average speed?
The time it takes for an object dropped from the top of cliff A to hit the water in the lake below is twice the time it takes for another object dropped from the top of cliff B to reach the lake. (a) The height of cliff A is (1) one-half, (2) two times, (3) four times that of cliff B. (b) If it
For the motion of a dropped object in free fall, sketch the general forms of the graphs of (a) v versus t and (b) y versus t.
You can perform a popular trick by dropping a dollar bill (lengthwise) through the thumb and forefinger of a fellow student. Tell your fellow student to grab the dollar bill as fast as possible, and he or she can have the dollar if able to catch it. (The length of a dollar is 15.7 cm, and the
A juggler tosses a ball vertically a certain distance. How much higher must the ball be tossed so as to spend twice as much time in the air?
A boy throws a stone straight upward with an initial speed of 15.0 m/s. What maximum height will the stone reach before falling back down?
In Exercise 64, what would be the maximum height of the stone if the boy and the stone were on the surface of the Moon, where the acceleration due to gravity is only one-sixth of that of the Earth’s?
The Petron as Twin Towers in Malaysia and the Chicago Sears Tower have heights of about 452 m and 443 m, respectively. If objects were dropped from the top of each, what would be the difference in the time it takes the objects to reach the ground?
In an air bag test, a car traveling at is remotely driven into a brick wall. Suppose an identical car is dropped onto a hard surface. From what height would the car have to be dropped to have the same impact as that with the brick wall?
You throw a stone vertically upward with an initial speed of 6.0 m/s from a third-story office window. If the window is 12 m above the ground, find (a) The time the stone is in flight and (b) The speed of the stone just before it hits the ground.
A Super Ball is dropped from a height of 4.00 m. Assuming the ball rebounds with 95% of its impact speed, (a) The ball would bounce to (1) less than 95%, (2) equal to 95%, or (3) more than 95% of the initial height? (b) How high will the ball go?
A train makes a round trip on a straight, level track. The first half of the trip is 300 km and is traveled at a speed of 75 km/h. After a 0.50 h layover, the train returns the 300 km at a speed of 85 km/h. What is the train’s (a) Average speed and (b) Average velocity?
In Fig. 2.25, a student at a window on the second floor of a dorm sees his math professor walking on the sidewalk beside the building. He drops a water balloon from 18.0 m above the ground when the professor is 1.00 m from the point directly beneath the window. If the professor is 1.70 m tall and
A photographer in a helicopter ascending vertically at a constant rate of 12.5 m/s accidentally drops a camera out the window when the helicopter is 60.0 m above the ground. (a) How long will the camera take to reach the ground? (b) What will its speed be when it hits?
The acceleration due to gravity on the Moon is about one-sixth of that on the Earth. (a) If an object were dropped from the same height on the Moon and on the Earth, the time it would take to reach the surface on the Moon is (1) √6, (2) 6, or (3) 36 times the time it would take on the Earth.
It takes 0.210 s for a dropped object to pass a window that is 1.35 m tall. From what height above the top of the window was the object released?
A tennis ball is dropped from a height of 10.0 m. It rebounds off the floor and comes up to a height of only 4.00 m on its first rebound. (Ignore the small amount of time the ball is in contact with the floor.) (a) Determine the ball’s speed just before it hits the floor on the way down. (b)
A pollution-sampling rocket is launched straight upward with rockets providing a constant acceleration of 12.0 m/s2 for the first 1000 m of flight. At that point the rocket motors cut off and the rocket itself is in free fall. Ignore air resistance. (a) What is the rocket’s speed when the
A test rocket containing a probe to determine the com-position of the upper atmosphere is fired vertically upward from an initial position at ground level. During the time t while its fuel lasts, the rocket ascends with a constant upward acceleration of magnitude 2g. Assume that the rocket travels
A car and a motorcycle start from rest at the same time on a straight track, but the motorcycle is 25.0 m behind the car (Fig. 2.27). The car accelerates at a uniform rate of 3.70 m/s2 and the motorcycle at a uniform rate of 4.40 m/s2.(a) How much time elapses before the motorcycle overtakes the
Two joggers run at the same average speed. Jogger A cuts directly north across the diameter of the circular track, while jogger B takes the full semicircle to meet his partner on the opposite side of the track. Assume their common average speed is and the track has a diameter of 150 m. (a) How
Many highways with steep downhill areas have “run-away truck” inclined paths just off the main roadbed. These paths are designed so that if a vehicle’s braking system gives out, the driver can steer it onto this incline (usually composed of loose gravel or sand). The idea is that the vehicle
A car travels three-quarters of a lap on a circular track of radius R. (a) The magnitude of the displacement is (1) less than R, (2) greater than R, but less than 2R, (3) greater than 2R. (b) If R = 50 m, what is the magnitude of the displacement?
The Taipei 101 Tower in Taipei, Taiwan is a 509-m (1667-ft), 101-story building (Fig. 2.28). The outdoor observation deck is on the 89th floor, and two high-speed elevators that service it reach a peak speed of 1008 m/min on the way up and 610 m/min on the way down. Assuming these peak speeds are
From street level, Superman spots Lois Lane in trouble— the evil villain, Lex Luthor, is dropping her from near the top of the Empire State Building. At that very instant, the Man of Steel starts upward at a constant acceleration to attempt a midair rescue of Lois. Assuming she was dropped from a
In the 1960s there was a contest to find the car that could do the following two maneuvers (one right after the other) in the shortest total time: First, accelerate from rest to 100 mi/h, (45.0 m/s), and then brake to a complete stop. (Ignore the reaction time correction that occurs between the
Let€™s investigate a possible vertical landing on Mars that includes two segments: free fall followed by a parachute deployment. Assume the probe is close to the surface, so the Martian acceleration due to gravity is constant at 3.00 m/s2. Suppose the lander is initially moving vertically
You are driving slowly in the right lane of a straight country road. For a while, a car to your left has lagged 50.0 m behind you at the same speed of 25.0 mi/h. Suddenly that car speeds up and passes you, traveling at a constant acceleration until it is 40.0 m in front of you 7.00 s later. (a)
A car is traveling on a straight, level road under wintry conditions. Seeing a patch of ice ahead of her, the driver of the car slams on her brakes and skids on dry pavement for 50 m, decelerating at 7.5 m/s2. Then she hits the icy patch and skids another 80 m before coming to rest. If her initial
On a water slide ride, you start from rest at the top of a 45.0-m-long incline (filled with running water) and accelerate down at 4.00 m/s2. You then enter a pool of water and skid along the surface for 20.0 m before stop-ping. (a) What is your speed at the bottom of the incline? (b) What is the
A toy rocket is launched (from the ground) vertically upward with a constant acceleration of 30.0 m/s2. After traveling 1000 m, its engines stop. When it reaches the very top of its motion, it falls for 0.500 s before a parachute deploys and it descends safely to the ground at the speed it has at
A Superball is dropped from a height of 2.5 m and rebounds off the floor to a height of 2.1 m. If the ball is in contact with the floor for 0.70 ms, determine (a) The direction and (b) Magnitude of the ball’s average acceleration due to the floor.
The interstate distance between two cities is 150 km. (a) If you drive the distance at the legal speed limit of 65 mi/h, how long would the trip take? (b) Suppose on the return trip you pushed it up to 80 mi/h (and didn’t get caught). How much time would you save?
A rifle is sighted-in so that a bullet hits the bull’s-eye of a target 1000 m away on the same level. (a) If the same sighting is used to shoot a target uphill, should one aim above, below, or right at the bull’s- eye? (b) How about shooting downhill?
Sitting in a parked bus, you suddenly look up at a bus moving alongside and it appears that you are moving. Why is this? How about with both buses moving in opposite directions?
When driving to the basket for a layup, a basketball player usually tosses the ball gently upward relative to herself. Explain why.
When you are riding in a fast-moving car, in what direction would you throw an object up so it will return to your hand? Explain.
Describe the motion of an object that is initially traveling with a constant velocity and then receives an acceleration of constant magnitude (a) In a direction parallel to the initial velocity, (b) In a direction perpendicular to the initial velocity, (c) That is always perpendicular to the
(a) Can a vector be less than one of its components? (b) How about equal to one of its components?

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