AP Physics Kinematics Review

A particle starts from rest at x =0 and moves for 10 s with an acceleration of +2.0 cm/s2. For the next 20 s, the acceleration of the particle is -1.0 cm/s2. What is the position of the particle at the end of this motion?

+3.0 m

Two passenger trains are passing each other on adjacent tracks. Train A is moving east with a speed of 13 m/s and train B is traveling west with a speed of 28 m/s. What is the velocity (magnitude and direction) of train A as seen by the passengers in train B? (or with respect to train B?) Take east as the positive direction.

+41 m/s

A car travels counterclockwise around a flat circle of radius 0.25 km at a constant speed of 20 m/s. When the car is at point A as shown in the figure, what is the car's acceleration?

1.6 m/s2, west

In physics Utopia a golf ball rolls off of a 500 m cliff. Initially it is traveling at 125 m/s. What is its range?

1250 m

A ball is thrown and follows a parabolic path, as shown above. It is launched with a speed of 30 m/s at an angle of 60o. Air friction is negligible. Point Q is the highest point on the path. What is the speed of the ball at point Q (the top) ?

15 m/s

A ball is thrown straight up from a point 2 m above the ground. The ball reaches a maximum height of 3 m above its starting point and then falls 5 m to the ground. When the ball strikes the ground, what is its displacement from its starting point?

2 m below

If air resistance is negligible, the speed of a 2 kg sphere that falls from rest through a vertical displacement of 0.2 m is most nearly

2 m/s

An object moving in a straight line has a velocity v in meters per second that varies with time t in seconds according to the following function. v = 4 + 0.5t^2 The instantaneous acceleration of the object at t = 2 seconds is

2 m/s2

A water balloon is dropped from a second story balcony. It hits the ground 2.0 seconds after it is released. How tall is the balcony?

20 m

An object released from rest at time t = 0 slides down a frictionless incline a distance of 1 meter during the first second. The distance traveled by the object during the time interval from t = 1 second to t = 2 seconds is

3 m

The coordinate of a particle in meters is given by mc027-1.jpg, where the time t is in seconds. The particle is momentarily at rest at t =

3.0 s

A truck traveled 400 meters north in 80 seconds, and then it traveled 300 meters east in 70 seconds. The magnitude of the average velocity of the truck was most nearly

3.3 m/s

A target T lies flat on the ground 3 m from the side of a building that is 10 m tall, as shown above. A student rolls a ball off the horizontal roof of the building in the direction of the target. Air resistance is negligible. The horizontal speed with which the ball must leave the roof if it is to strike the target is most nearly

3/sqrt(2)

In the absence of air resistance, a thrown ball will travel the greatest distance across the ground if it is thrown at an angle of about

45 degrees

A truck traveled 400 meters north in 40 seconds, stopped at a red light for 30 seconds, and then it traveled 4.0 m/s north for 50 seconds. The magnitude of the average velocity of the truck was most nearly

5.0 m/s

Neglecting the effect of air resistance a stone dropped off a 180-m high building lands on the ground in:

6 s

A river has a steady speed of 0.30 m/s. A student swims downstream a distance of 1.2 km W and returns to the starting point. If the student swims with respect to the water at a constant speed and the downstream portion of the swim requires 20 minutes, how much time is required for the entire swim?

70 minutes

A velocity vector has magnitude of 8.0 m/s and direction of 30o N of E. Expressed in unit vector notation. it would be:

8sqrt(3)/2i + 4j

A 500-kilogram sports car accelerates uniformly from rest, reaching a speed of 30 meters per second in 6 seconds. During the 6 seconds, the car has traveled a distance of

90 m

A ball of mass m is attached to the end of a string of length Q as shown above. The ball is released from rest from position P. where the string is horizontal. It swings through position Q. where the string is vertical, and then to position R. where the string is again horizontal. What are the directions of the acceleration vectors of the ball at positions Q and R (respectively)? Position Q Position R

Upward, Downward

Suppose you are in a car that is going around a curve. The speedometer reads a constant 30 miles per hour. Which of the following is NOT true?

Your velocity is constant

A racing car is moving around the circular track of radius 300 meters shown above. At the instant when the car's velocity is directed due east, its acceleration is directed due south and has a magnitude of 3 meters per second squared. When viewed from above, the car is moving

clockwise at 30 m/s

A figure of a dancer on a music box moves counterclockwise at constant speed around the path shown above. The path is such that the lengths of the segments, PQ, QR, RS, and SP are equal. Arcs QR and SP are semicircles. Which of the following best represents the magnitude of the dancers acceleration as a function of time t during one trip around the path, beginning at point P?

graph two rectanges, second is missing a side

The graph above shows the velocity v as a function of time t for an object moving in a straight line. Which of the following graphs shows the corresponding displacement x as a function of time t for the same time interval?

graph with "s" curve

In the absence of air friction, an object dropped near the surface of the Earth experiences a constant acceleration of about 9.8 m/s2. This means that the

speed of the object increases 9.8 m/s during each second

Two projectiles are launched with the same initial speed from the same location, one at a 30o angle and the other at a 60o angle with the horizontal. They land at the same height at which they were launched. If air resistance is negligible, how do the projectiles' respective maximum heights, H30 and H60, and times in the air, T30 and T60, compare with each other? Maximum Height Time in Air

H30 < H60, T30 < T60

Consider the following five graphs (note the axes carefully). Which of these represents motion at constant speed?

I and IV only

In which of the following situations would an object be accelerated? I. It moves in a straight line at constant speed. II. It moves with uniform circular motion. III. It travels as a projectile in a gravitational field with negligible air resistance.

II and III only

A student in the front of a school bus tosses a ball to another student in the back of the bus while the bus is moving forward at constant velocity. The speed of the ball as seen by a stationary observer in the street:

may be either greater or smaller than that observed inside the bus.

An airplane flying into a head wind loses ground speed, and an airplane flying with the wind gains ground speed. If an airplane flies at right angles to the wind, then ground speed is

more

Throughout a time interval, while the speed of a particle increases as it moves along the x axis, its velocity and acceleration might be:

negative and negative, respectively

Starting from rest, a vehicle accelerates on a straight level road at the rate of 4.0 m/s2 for 5.0 s. What is the speed of the vehicle at the end of this time interval?

20 m/s

A particle moves along the x-axis with a non-constant acceleration described by a = 12t, where a is in meters per second squared and t is in seconds. If the particle starts from rest so that its speed v and position x are zero when t = 0, where is it located when t = 2 seconds?

x = 16m

The displacement x of an object moving along the x-axis is shown above as a function of time t. The acceleration of this object must be

zero

A rock is dropped from the top of a 45-meter tower, and at the same time a ball is thrown from the top of the tower in a horizontal direction. Air resistance is negligible. The ball and the rock hit the level ground a distance of 30 meters apart. The horizontal velocity of the ball thrown was most nearly (A) (B) (C) (D) (E)

10 m/s

The following pairs of equations show how the x- and y-coordinates of a particle vary with time t. In the equations, A, B, and w are nonzero constants. Choose the pair of equations that best answers each of the following questions. A choice may be used once, more than once, or not at all. (A) x = Acoswt y = Asinwt (B) x = Acoswt y = 2Acoswt (C) x = At y = Bt (D) x = At2 y = Bt2 (E) x = At y = Bt2 Which pair of equations can describe the path of a particle moving with an acceleration that is perpendicular to the velocity of the particle at t = 0 and remains constant in magnitude and direction?

E

Two vectors, R and S, are known: R(down) and S(right) If vector S is subtracted from vector R, the vector T = R - S is

b left down

An object slides off a roof 10 meters above the ground with an initial horizontal speed of 5 meters per second as shown above. The time between the object's leaving the roof and hitting the ground is most nearly

sqrt(2) s

A particle moves at a constant speed in a circular path with a radius of r m. If the particle makes four revolutions each second, what is the magnitude of its acceleration?

(64p2r) m/s2

A body moving in the positive x direction passes the origin at time t = 0. Between t = 0 and t = 1 second, the body has a constant speed of 24 meters per second. At t = 1 second, the body is given a constant acceleration of 6 meters per second squared in the negative x direction. The position x of the body at t = 11 seconds is

- 36 m

A box slides across a horizontal floor in a straight line. It starts with a speed of 5 m/s and slows down to 2 m/s after 3 seconds. What is the average acceleration over this interval?

-1 m/s2

In 2.0 s, a particle moving with constant acceleration along the x axis goes from x = 10 m to x = 50 m. The velocity at the end of this time interval is 10 m/s. What is the acceleration of the particle?

-10 m/s2

A body moving in the positive x direction passes the origin at time t = 0. Between t = 0 and t = 1 second, the body has a constant speed of 24 meters per second. At t = 1 second, the body is given a constant acceleration of 6 meters per second squared in the negative x direction. The position x of the body at t = 11 seconds is

-36 m

An object is dropped from rest from the top of a 400 m cliff on Earth. If air resistance is negligible, what is the distance the object travels during the first 6s of its fall?

180 m

A ball thrown vertically from ground level is caught 3.0 s later by a person on a balcony which is 15 m above the ground. Determine the initial speed of the ball.

20 m/s

A diver initially moving horizontally with speed v dives off the edge of a vertical cliff and lands in the water a distance d from the base of the cliff. How far from the base of the cliff would the diver have landed if the diver initially had been moving horizontally with speed 2v?

2d

What is the minimum resultant possible when adding a 3-unit vector to an 8-unit vector?

5

Starting from rest, a vehicle accelerates on a straight level road at the rate of 4.0 m/s2 for 5.0 s. What is the total distance the vehicle travels during this time interval?

50 m

A projectile is fired from the surface of the Earth with a speed of 200 meters per second at an angle of 30° above the horizontal. If the ground is level, what is the maximum height reached by the projectile?

500 m

An object is released from rest on a planet that has no atmosphere. The object falls freely for 3.0 meters in the first second. What is the magnitude of the acceleration due to gravity on the planet?

6.0 m/s2

An object moving in a straight line has a velocity v in meters per second that varies with time t in seconds according to the following function. v = 4 + 0.5t^2 The displacement of the object between t = 0 and t = 6 seconds is

60 m

The graph above shows the velocity versus time for an object moving in a straight line. At what time after t = 0 does the object again pass through its initial position?

Between 1 and 2 s

What do acceleration and velocity have in common?

Both are vectors

The following pairs of equations show how the x- and y-coordinates of a particle vary with time t. In the equations, A, B, and w are nonzero constants. Choose the pair of equations that best answers each of the following questions. A choice may be used once, more than once, or not at all. (A) x = Acoswt y = Asinwt (B) x = Acoswt y = 2Acoswt (C) x = At y = Bt (D) x = At2 y = Bt2 (E) x = At y = Bt2 Which pair of equations can describe the path of a particle moving with zero acceleration?

C

At time t = 0, car X traveling with speed v0 passes car Y. which is just starting to move. Both cars then travel on two parallel lanes of the same straight road. The graphs of speed v versus time t for both cars are shown above. Which of the following is true at time t = 20 seconds?

Car Y is behind car X

At time t = 0, car X traveling with speed v0 passes car Y. which is just starting to move. Both cars then travel on two parallel lanes of the same straight road. The graphs of speed v versus time t for both cars are shown above. From time t = 0 to time t = 40 seconds, the areas under both curves are equal. Therefore, which of the following is true at time t = 40 seconds?

Car Y is passing car X.

Under which conditions is it true that the magnitude of average velocity would be smaller than average speed.

The particle moved in the +x direction then reversed direction.

Two people are in a boat that is capable of a maximum speed of 5 kilometers per hour in still water, and wish to cross a river 1 kilometer wide to a point directly across from their starting point. If the speed of the water in the river is 5 kilometers per hour, how much time is required for the crossing?

The point directly across from the starting point cannot be reached under these conditions

An object is shot vertically upward into the air with a positive initial velocity. Which of the following correctly describes the velocity and acceleration (respectively) of the object at its maximum elevation? Velocity Acceleration

Zero, Negative

A rock of mass m is thrown horizontally off a building from a height h, as shown above. The speed of the rock as it leaves the thrower's hand at the edge of the building is v0. How much time does it take the rock to travel from the edge of the building to the ground?

sqrt(2h/g)

A ball is thrown and follows a parabolic path, as shown above. Air friction is negligible. Point Q is the highest point on the path. Which of the following best indicates the direction of the acceleration, if any, of the ball at point Q ?

c (straight down)

A ball is thrown and follows a parabolic path, as shown above. It is launched with a speed of 30 m/s at an angle of 60o. Air friction is negligible. Point Q is the highest point on the path. Which of the following best indicates the direction of the acceleration, if any, of the ball at point Q ?

c (straight down)

Which of the following pairs of graphs shows the distance traveled versus time and the speed versus time for an object uniformly accelerated from rest

curve up, constant up

Vectors V1, and V2 shown above have equal magnitudes. The vectors represent the velocities of an object at times t1, and t2, respectively. The average acceleration of the object between time t1 and t2 was (A) (B) (C) (D) (E)

directed north of west

A ball is thrown into the air at some angle between 10 degrees and 90 degrees. At the very top of the ball's path, its velocity is

entirely horizontal

An object is thrown vertically upwards in a region where g is constant and air resistance is negligible. Its speed is recorded from the moment it leaves the thrower's hand until it reaches its maximum height. Which of the following graphs best represents the object's speed v versus time t.

graph constant down

The graph above shows velocity v versus time t for an object in linear motion. Which of the following is a possible graph of position x versus time t for this object? (A) (B) (C) (D) (E)

graph hump

Which of the following graphs of position d versus time t corresponds to motion of an object in a straight line with positive acceleration?

graph increasing up

Each of the three graphs above represents acceleration versus time for an object that already has a non-zero positive velocity at time t1. Which graphs show an object whose speed is increasing for the entire time interval between t1 and t2?

graphs I, II, and III

An object is thrown with velocity v from the edge of a cliff above level ground. Neglect air resistance. In order for the object to travel a maximum horizontal distance from the cliff before hitting the ground, the throw should be at an angle q with respect to the horizontal of

greater than zero but less than 45o above the horizontal

Two cars are traveling around identical circular racetracks. Car A travels at a constant speed of 20 m/s. Car B starts at rest and speeds up with constant tangential acceleration until its speed is 40 m/s. When car B has the same (tangential) velocity as car A, it is always true that:

it has the same centripetal acceleration as car A.

A ball is thrown straight up, at the top of its path the magnitude of its acceleration is

m/s^2

Three students leaning over the edge of a cliff each release a ball in a different way Ball A is dropped from rest Ball B is thrown downward with an initial speed of 10 m/s Ball C is thrown upward with an initial speed of 10 m/s Since the students were leaning over the edge, all three balls (including the one that was thrown straight up) eventually strike the ground at the base of the cliff. Which of the five choices below correctly compares the speeds with which each of the balls strikes the ground?

speed of ball A < speed of ball B = speed of ball C

At a particular instant, a stationary observer on the ground sees a package falling with speed v1 at an angle to the vertical. To a pilot flying horizontally at constant speed relative to the ground, the package appears to be falling vertically with a speed v2 at that instant. What is the speed of the pilot relative to the ground?

sqrt(v1^2-v2^2)

Two cooks standing side by side in a restaurant pull their beaters out of the dough at the same instant. A glob of dough flies off each beater. Each glob lands on the top of a tin the same horizontal distance away and at its initial height. However, one lands later than the other. The explanation is that they left the beaters at angles q1 and q2 such that:

theta1 + theta2 = 90

A ball is thrown and follows the parabolic path shown above. Air friction is negligible. Point Q is the highest point on the path. Points P and R are the same height above the ground. How do the speeds of the ball at the three points compare?

vQ< vP = vR

A rock is thrown from the edge of a cliff with an initial velocity v0 at an angle theta with the horizontal as shown above. Point P is the highest point in the rock's trajectory and point Q is level with the starting point. Assume air resistance is negligible. Which of the following correctly describes the horizontal and vertical speeds and the acceleration (respectively) of the rock at point P ? Horizon- tal Speed Vertical Speed Acceleration

vcosx 0 g

A rock is thrown from the edge of a cliff with an initial velocity v0 at an angle q with the horizontal as shown above. Point P is the highest point in the rock's trajectory and point Q is level with the starting point. Assume air resistance is negligible. Which of the following correctly describes the horizontal and vertical speeds and the acceleration of the rock at point Q ? Horizon- tal Speed Vertical Speed Acceleration

vcosx vsinx g

A particle moves along the x-axis with a non-constant acceleration described by a = 18t, where a is in meters per second squared and t is in seconds. If the particle starts from rest so that its speed v and position x are zero when t = 0, where is it located when t = 2 seconds?

x = 24 m

The following pairs of equations show how the x- and y-coordinates of a particle vary with time t. In the equations, A, B, and w are nonzero constants. Choose the pair of equations that best answers each of the following questions. A choice may be used once, more than once, or not at all. (A) x = Acoswt y = Asinwt (B) x = Acoswt y = 2Acoswt (C) x = At y = Bt (D) x = At2 y = Bt2 (E) x = At y = Bt2 Which pair of equations can describe the path of a particle that moves with a constant speed and with a nonzero acceleration that is constant in magnitude?

A

Two balls, projected at different times so they don't collide, have trajectories A and B, as shown below. Which statement is correct? (note: this is a diagram of position, not a graph of displacement vs time)

Ball B is in the air for a longer time than ball A.

Two identical balls are held side by side at the top of a tall building. You drop one ball, A. A little later you throw the second ball, B, down with an initial speed. The second ball falls down along a line parallel to the path of the first ball and passes it. At the instant ball B passes ball A:

it has the same displacement and the same acceleration as A.