AP Physics Sem 1
An object with an unknown initial velocity has a constant acceleration with components ax=8m/s2 and ay=0. Which of the following is a possible expression for the position of this object, in meters, for both the x and y directions as functions of time?
x=4t^2 and y=8t
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 ω 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. 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?
x=Acosωt y=Asinωt
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 ω 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. Which pair of equations can describe the path of a particle moving with zero acceleration?
x=At y=Bt
The graph above shows velocity as a function of time for an object moving in a straight line. What is the average acceleration of the object during the first 88 seconds?
+0.5m/s2
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 6 s of its fall?
180 m
The position of a toy locomotive moving on a straight track along the x-axis is given by the equation x = t^3 - 6t^2 + 9t, where x is in meters and t is in seconds. The net force on the locomotive is equal to zero when t is equal to
2 s
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
The graph above shows the speed v of a car on a horizontal road as a function of time t for 12 seconds. The distance traveled by the car during this time interval is most nearly
200 m
An object of mass m1 initially hangs from a rod of length L and negligible mass that can pivot freely in the vertical plane, as shown in the figure above. A projectile of mass m2 is moving to the right at speed v when it strikes the hanging object and then drops straight down. The hanging object then swings upward and comes to rest at the top of a half circle as shown. What is the initial speed of the projectile v?
2m1sqrt(GL)/m2
A projectile is launched from level ground with an initial speed v0 at an angle Θ with the horizontal. If air resistance is negligible, how long will the projectile remain in the air?
2v0 sinΘ/g
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/√2. m/s
A spring has a force constant of 100 N/m and an unstretched length of 0.07 m. One end is attached to a post that is free to rotate in the center of a smooth table, as shown in the top view above. The other end is attached to a 1 kg disc moving in uniform circular motion on the table, which stretches the spring by 0.03 m. Friction is negligible. What is the centripetal force on the disc?
3N
A block of mass 3 kg, initially at rest, is pulled along a frictionless, horizontal surface with a force shown as a function of time t by the graph above. The speed of the block at t = 2s is
4/3 m/s
A block of mass 3 kg, initially at rest, is pulled along a frictionless, horizontal surface with a force shown as a function of time t by the graph above. The acceleration of the block at t = 2s is
4/3 m/s2
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
The position of an object is given by the equation x = 3.0 t^2 + 1.5 t + 4.5, where x is in meters and t is in seconds. What is the instantaneous acceleration of the object at t = 3.0 s?
6.0 m/s2
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 spring has a force constant of 100 N/m and an unstretched length of 0.07 m. One end is attached to a post that is free to rotate in the center of a smooth table, as shown in the top view above. The other end is attached to a 1 kg disc moving in uniform circular motion on the table, which stretches the spring by 0.03 m. Friction is negligible. What is the work done on the disc by the spring during one full circle?
A) 0 J
A student holds one end of a string in a fixed position. A ball of mass 0.2 kg attached to the other end of the string moves in a horizontal circle of radius 0.5 m with a constant speed of 5 m/s. How much work is done on the ball by the string during each revolution?
A) 0J
An object of mass 4 kg4 kg initially at rest on a surface has both kinetic and potential energies equal to zero. It is then lifted under the influence of both nonconservative forces and the conservative force of gravity. The nonconservative forces do +40 J+40 J of work on the object. The conservative force does −22 J−22 J of work. The speed of the object at the end of the motion is most nearly
A) 3.0 m/s
The following graph represents a hypothetical potential energy curve for a particle of mass m. If the potential energy function is given by U(r) = br -3/2 + c, where b and c are constants, which of the following is an expression for the force on the particle?
A) 3b/2 * r^−5/2
The momentum p of a moving object as a function of time t is given by the expression p = kt3, where k is a constant. The force causing this motion is given by the expression
A) 3kt^2
Two identical massless springs are hung from a horizontal support. A block of mass 1.2 kilograms is suspended from the pair of springs, as shown above. When the block is in equilibrium, each spring is stretched an additional 0.15 meter. The force constant of each spring is most nearly
A) 40 N
Two identical massless springs are hung from a horizontal support. A block of mass 1.2 kilograms is suspended from the pair of springs, as shown above. When the block is in equilibrium, each spring is stretched an additional 0.15 meter. When the block is set into oscillation with amplitude A, it passes through its equilibrium point with a speed v. In which of the following cases will the block, when oscillating with amplitude A, also have speed v when it passes through its equilibrium point? 1) The block is hung from only one of the two springs. 2) The block is hung from the same two springs, but the springs are connected in series rather than in parallel. 3) A 0.5-kilogram mass is attached to the block.
A) None
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) Parabola with max
An object is released from rest at time t = 0 and falls through the air, which exerts a resistive force such that the acceleration a of the object is given by a = g - bV, where V is the object's speed and b is a constant. If limiting cases for large and small values of t are considered, which of the following is a possible expression for the speed of the object as an explicit function of time?
A) V = g(1 - e^-bt)/b
If one knows only the constant resultant force acting on an object and the time during which this force acts, one can determine the
A) change in momentum of the object
When an object is moved from rest at point A to rest at point B in a gravitational field, the net work done by the field depends on the mass of the object and
A) the positions of A and B only
A box of mass M is sliding along a rough surface with initial velocity v. After traveling a distance x it comes to rest due to the friction between the box and the ground. What is the coefficient of kinetic friction between the box and the ground?
A) v^2/(2gx)
A car travels forward with constant velocity. It goes over a small stone, which gets stuck in the groove of a tire. The initial acceleration of the stone, as it leaves the surface of the road, is
A) vertically upward
The object of mass m shown above is dropped from rest near Earth's surface and experiences a resistive force of magnitude kv , where v is the speed of the object and k is a constant. Which of the following expressions can be used to find v as a function of time t ? (Assume that the direction of the gravitational force is positive.)
A) ∫v0 dv/(mg−kv) = ∫t0 dt/m
As shown above, two students sit at opposite ends of a boat that is initially at rest. The student in the front throws a heavy ball to the student in the back. What is the motion of the boat at the time immediately after the ball is thrown and, later, after the ball is caught? (Assume that air and water friction are negligible.)
After the throw: Boat moves forward After the catch: Boat doesn't move
A 5 kg object is propelled from rest at time t = 0 by a net force F that always acts in the same direction. The magnitude of F in newtons is given as a function of t in seconds by F = 0.5t. What is the speed of the object at t = 4 s?
B) .8 m/s
A ball is thrown upward. At a height of 10 meters above the ground, the ball has a potential energy of 50 joules (with the potential energy equal to zero at ground level) and is moving upward with a kinetic energy of 50 joules. Air friction is negligible. The maximum height reached by the ball is most nearly
B) 20 m
A frictionless pendulum of length 3 m swings with an amplitude of 10°. At its maximum displacement, the potential energy of the pendulum is 10 J. What is the kinetic energy of the pendulum when its potential energy is 5 J?
B) 5J
Two pucks moving on a frictionless air table are about to collide, as shown above. The 1.5 kg puck is moving directly east at 2.0 m/s. The 4.0 kg puck is moving directly north at 1.0 m/s. What is the total kinetic energy of the two-puck system before the collision?
B) 5J
A person holds a portable fire extinguisher that ejects 1.0 kg of water per second horizontally at a speed of 6.0 m/s. What horizontal force in newtons must the person exert on the extinguisher in order to prevent it from accelerating?
B) 6N
A ball initially moves horizontally with velocity vi , as shown above. It is then struck by a stick. After leaving the stick, the ball moves vertically with a velocity v𝑓 , which is smaller in magnitude than vi . Which of the following vectors best represents the direction of the average force that the stick exerts on the ball?
B) Arrow pointed slightly above west
A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible mass, as shown above.Which of the five lettered points represents the center of mass of the sphere-rod combination?
B) B
A force F is exerted by a broom handle on the head of the broom, which has a mass m. The handle is at an angle θ to the horizontal, as shown above. The work done by the force on the head of the broom as it moves a distance d across a horizontal floor is
B) Fd cos θ
A wheel with rotational inertia I is mounted on a fixed, frictionless axle. The angular speed 𝜔 of the wheel is increased from zero to 𝜔𝑓 in a time interval T. What is the average power input to the wheel during this time interval?
B) Iω^2f/2T
Four identical, uniform sheets of aluminum are welded together, as shown above. Which of the following points best represents the center of mass of the system?
B) Point B
A block of mass m is initially sliding with speed v0 on a horizontal frictionless surface, as shown above. It makes an elastic, head-on collision with another block of mass 2m that is initially at rest. Which of the following correctly shows the motion of the blocks after the collision?
B) m at v0/3 to the left and 2m 2v/3 to the right
Two identical blocks each start at rest from the same height and slide down surfaces inclined at the same angle θ, as shown. In Figure 1, there is negligible friction between the block and the surface, while in Figure 2 , the surface is rough and the coefficient of kinetic friction between the block and the surface is μ . The acceleration of the block in Figure 1 is a1, and the acceleration of the block in Figure 2 is a2. The value of the ratio a1/a2 is
B) sinθ/(sinθ−μcosθ)
A particle that is constrained to move along the x-axis is acted upon by a conservative force F that varies according to the function F(x)=−k/x^3, where k is a positive constant with units of N⋅m^3. Which of the following is the correct expression for the change in potential energy as the particle moves from x=x1 to x=x2.
B) ΔU=1/2k(1/x(2->1) − 1/x(2->2))
A block of mass m is placed against the inner wall of a hollow cylinder of radius R that rotates about a vertical axis with a constant angular velocity ω, as shown above. In order for friction to prevent the mass from sliding down the wall, the coefficient of static friction μ between the mass and the wall must satisfy which of the following inequalities?
B) μ ≥ g/(ω^2R)
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 its segments, PQ, QR, RS, and SP, are equal. Arcs QR and SP are semicircles. Which of the following best represents the magnitude of the dancer's acceleration as a function of time t during one trip around the path, beginning at point P ?
Block Pattern: Start at 0
An object of mass 4 kg4 kg initially at rest on a surface has both kinetic and potential energies equal to zero. It is then lifted under the influence of both nonconservative forces and the conservative force of gravity. The nonconservative forces do +40 J of work on the object. The conservative force does −22 J of work. The potential energy of the object after the motion is
C) + 22 J
When a block slides a certain distance down an incline, the work done by gravity is 300 J. What is the work done by gravity if this block slides the same distance up the incline?
C) -300 J
The graph above shows the force on an object of mass M as a function of time. For the time interval 0 to 4 s, the total change in the momentum of the object is
C) 0 kg m/s
A box of mass 5 kg is at rest on a rough horizontal surface. The coefficients of static and kinetic friction between the surface and the box are 0.3 and 0.25, respectively. A 10 N horizontal force is applied to the box. What is the frictional force acting on the box?
C) 10 N
A 1000 W electric motor lifts a 100 kg safe at constant velocity. The vertical distance through which the motor can raise the safe in 10 s is most nearly
C) 10m
A model rocket of mass 0.5 kg is launched from the ground. From time t=0 to t=3s, the rocket's engines exert an impulse of 45 N⋅s vertically on the rocket. Assuming the mass of the rocket remains constant, the average acceleration of the rocket during this time interval is most nearly
C) 20 m/s2
As shown in the top view above, a disc of mass m is moving horizontally to the right with speed v on a table with negligible friction when it collides with a second disc of mass 2m. The second disc is moving horizontally to the right with speed v2 at the moment of impact. The two discs stick together upon impact. The speed of the composite body immediately after the collision is
C) 2v/3
Two pucks moving on a frictionless air table are about to collide, as shown above. The 1.5 kg puck is moving directly east at 2.0 m/s. The 4.0 kg puck is moving directly north at 1.0 m/s. What is the magnitude of the total momentum of the two-puck system after the collision?
C) 5J
Three blocks of masses 3m, 2m, and m are connected to strings A, B, and C as shown above. The blocks are pulled along a rough surface by a force of magnitude F exerted by string C. The coefficient of friction between each block and the surface is the same. Which string must be the strongest in order not to break?
C) C
If F1 is the magnitude of the force exerted by the Earth on a satellite in orbit about the Earth and F2 is the magnitude of the force exerted by the satellite on the Earth, then which of the following is true?
C) F1 is equal to F2.
A box is sent up a ramp with an initial speed of v0, as shown in the figure above. The box stops before reaching the top of the ramp and then slides back down the ramp. There is friction between the box and the ramp. If the positive direction is up the ramp, which of the following graphs best represents the velocity v of the box as a function of time t as it travels along the ramp?
C) Linear Line down then slight negative slope
An object is thrown vertically upward 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 u versus time t ?
C) Linear Negative Line
A dart gun is used to fire two rubber darts with different but unknown masses, M1 and M2. The gun exerts the same constant force on each dart, but its magnitude F is unknown. The magnitudes of the accelerations of both darts, a1 and a2, respectively, are measured. Which of the following can be determined from these data?
C) The ratio of M1 and M2 only
A small box is on a ramp tilted at an angle 𝜽 above the horizontal. The box may be subject to the following forces: frictional ( 𝑓 ), gravitational ( 𝑚𝘨 ), pulling or pushing ( 𝐹𝑃 ) , and normal ( 𝑁 ). In the following free-body diagrams for the box, the lengths of the vectors are proportional to the magnitudes of the forces. Which figure best represents the free-body diagram for the box if it is at rest on the ramp?
C) Tilted N, vertical MG, short f
A small box is on a ramp tilted at an angle 𝜽 above the horizontal. The box may be subject to the following forces: frictional ( 𝑓 ), gravitational ( 𝑚𝘨 ), pulling or pushing ( 𝐹𝑃 ) , and normal ( 𝑁 ). In the following free-body diagrams for the box, the lengths of the vectors are proportional to the magnitudes of the forces. Which figure best represents the free-body diagram for the box if it is sliding down the ramp at constant speed?
C) Tilted N, vertical MG, short f
A weight lifter lifts a mass m at constant speed to a height h in time t. How much work is done by the weight lifter?
C) mgh
The following graph represents a hypothetical potential energy curve for a particle of mass m. If the particle is released from rest at position r0 , its speed at position 2r0 is most nearly
C= sqrt(4Uo/m)
A block of mass m is accelerated across a rough surface by a force of magnitude F that is exerted at an angle 𝜙 with the horizontal, as shown above. The frictional force on the block exerted by the surface has magnitude f. What is the acceleration of the block?
D) (Fcosϕ−f)/m
A disc of mass m slides with negligible friction along a flat surface with a velocity v. The disc strikes a wall head-on and bounces back in the opposite direction with a kinetic energy one-fourth of its initial kinetic energy. What is the final velocity of the disc?
D) -v/2
The net force F on a particle as a function of time t is given by the equation F=6kt^2, where k is a positive constant in units of N/s^2 Which of the following could represent the change in momentum Δp as a function of time t?
D) 2kt^3
An object weighing 300 N is suspended by means of two cords, as shown above. The tension in the horizontal cord is
D) 300 N
To stretch a certain nonlinear spring by an amount x requires a force F given by F = 40x - 6x^2 , where F is in newtons and x is in meters. What is the change in potential energy when the spring is stretched 2 meters from its equilibrium position?
D) 64 J
A person of mass 70 kg is standing in an elevator that is moving downward. The speed decreases uniformly from 4.0 m/s to zero in 2.0 s. What is the normal force acting on the person?
D) 840 N
Two balls are on a frictionless horizontal tabletop. Ball X initially moves at 10 meters per second, as shown in Figure I above. It then collides elastically with identical ball Y, which is initially at rest. After the collision, ball X moves at 6 meters per second along a path at 53° to its original direction, as shown in Figure II above. Which of the following diagrams best represents the motion of ball Y after the collision?
D) Angled 37 degrees to the bottom at 8 m/s
A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible mass, as shown above. The sphere-rod combination can be pivoted about an axis that is perpendicular to the plane of the page and that passes through one of the five lettered points. Through which point should the axis pass for the moment of inertia of the sphere-rod combination about this axis to be greatest?
D) D
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?
D) Positive Slope. Curve up, straight line, curve to asymptote
A small mass is released from rest at a very great distance from a larger stationary mass. Which of the following graphs best represents the gravitational potential energy U of the system of the two masses as a function of t ?
D) Start at origin and negative exponential graph
An object of mass m moves with acceleration a down a frictionless incline that makes an angle with the horizontal, as shown above. If N is the normal force exerted by the plane on the block, which of the following is correct?
D) a=g sinθ
For a particular nonlinear spring, the relationship between the magnitude of the applied force F and the resultant displacement x from equilibrium is given by the equation F = kx2. What is the amount of work done by stretching the spring a distance x0?
E = 1/3 k 3->0
Two blocks of masses M and m, with M > m, are connected by a light string. The string passes over a frictionless pulley of negligible mass so that the blocks hang vertically. The blocks are then released from rest. What is the acceleration of the block of mass M ?
E) (M−m)/(M+m) * g
A person is standing at one end of a uniform raft of length L that is floating motionless on water, as shown above. The center of mass of the person-raft system is a distance d from the center of the raft. The person then walks to the other end of the raft. If friction between the raft and the water is negligible, how far does the raft move relative to the water?
E) 2d
A 2000 kg car, initially at rest, is accelerated along a horizontal roadway at 3 m/s2. What is the average power required to bring the car to a final speed of 20 m/s?
E) 6 x 10^4 W
Three identical disks are initially at rest on a frictionless, horizontal table with their edges touching to form a triangle, as shown in the top view above. An explosion occurs within the triangle, propelling the disks horizontally along the surface. Which of the following diagrams shows a possible position of the disks at a later time? (In these diagrams, the triangle is shown in its original position.)
E) All balls are farthest away
A wheel with rotational inertia I is mounted on a fixed, frictionless axle. The angular speed 𝜔 of the wheel is increased from zero to 𝜔𝑓 in a time interval T. What is the average net torque on the wheel during this time interval?
E) IWf/T
A conservative force has the potential energy function U ( x ), shown by the graph above. A particle moving in one dimension under the influence of this force has kinetic energy 1.0 joule when it is at position x1. Which of the following is a correct statement about the motion of the particle?
E) It cannot reach either x0 or x2.
The graph above shows the force of gravity on a small mass as a function of its distance R from the center of the Earth of radius Re, if the Earth is assumed to have a uniform density. The work done by the force of gravity when the small mass approaches Earth from far away and is placed into a circular orbit of radius R2 is best represented by the area under the curve between
E) R = R2 and R = ∞
A 2 kg ball collides with the floor at an angle 𝜽 and rebounds at the same angle and speed as shown above. Which of the following vectors represents the impulse exerted on the ball by the floor?
E) Straight Upward
A skier slides at constant speed down a slope inclined at an angle ϕ to the horizontal, as shown above. If air resistance is negligible, the coefficient of friction µ between the skis and the snow is equal to
E) Tan ϕ
A small box is on a ramp tilted at an angle 𝜽 above the horizontal. The box may be subject to the following forces: frictional ( 𝑓 ), gravitational ( 𝑚𝘨 ), pulling or pushing ( 𝐹𝑃 ) , and normal ( 𝑁 ). In the following free-body diagrams for the box, the lengths of the vectors are proportional to the magnitudes of the forces. Which figure best represents the free-body diagram for the box if it is accelerating up the ramp?
E) Tilted N, vertical MG, Longer Fp, short f
A block of mass m is accelerated across a rough surface by a force of magnitude F that is exerted at an angle 𝜙 with the horizontal, as shown above. The frictional force on the block exerted by the surface has magnitude f. What is the coefficient of friction between the block and the surface?
E) f/ (mg−Fsinϕ)
Objects 1 and 2 have the same momentum. Object 1 can have more kinetic energy than object 2 if, compared with object 2, it
E) is moving faster
All of the following are units of power EXCEPT
E) kilogram meters per second
A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above. If the plane has friction so that the sphere rolls without slipping, what is the speed vcm of the center of mass at the bottom of the incline?
E) sqrt((2Mghr^2)/ I + Mr^2)
An ant of mass m clings to the rim of a flywheel of radius r, as shown above. The flywheel rotates clockwise on a horizontal shaft S with constant angular velocity 𝜔. As the wheel rotates, the ant revolves past the stationary points I, II, III, and IV. The ant can adhere to the wheel with a force much greater than its own weight. What is the magnitude of the minimum adhesion force necessary for the ant to stay on the flywheel at point III?
E) 𝑚𝜔^2𝑟 + 𝑚𝘨
A person is riding a distance r from the center of a rotating platform, as shown in Figure 1. The person is moving with a constant linear speed v. For the view looking down on the person in Figure 2, which of the following best shows the direction of the net force exerted by the platform on the person?
Horizontal Right
A student is testing the kinematic equations for uniformly accelerated motion by measuring the time it takes for light-weight plastic balls to fall to the floor from a height of 3 m in the lab. The student predicts the time to fall using g as 9.80 m/s2 but finds the measured time to be 35% greater. Which of the following is the most likely cause of the large percent error?
The acceleration of the plastic balls is not uniform.
An object is shot vertically upward into the air with a positive initial velocity. Which of the following correctly describes the velocity and acceleration of the object at its maximum elevation?
Velocity: 0 Acceleration: Negative
A particle is initially at rest on the x-axis at the +3.0 m+3.0 m mark. It then moves toward the origin with increasing speed. Which of the following correctly indicates the proper sign of its velocity and acceleration?
Velocity: Negative Acceleration: Positive
The velocity of a projectile at launch has a horizontal component vh and a vertical component vv. Air resistance is negligible. When the projectile is at the highest point of its trajectory, which of the following show the vertical and horizontal components of its velocity and the vertical component of its acceleration?
Vertical Velocity: Vv (V sub v) Horizontal Velocity: 0 Vertical Acceleration: 0
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 𝜽 with respect to the horizontal of
greater than zero but less than 45° above the horizontal
A student throws a projectile horizontally at a target a horizontal distance R away. The projectile is released from a height H above the ground and strikes the target a height h below the release point, as shown above. Which of the following indicates the values that must be known for a student to calculate the initial speed of the projectile?
h and R only
A spring-loaded gun can fire a projectile to a height h if it is fired straight up. If the same gun is pointed at an angle of 45° from the vertical, what maximum height can now be reached by the projectile?
h/√2
A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above. If the plane is frictionless, what is the speed vcm of the center of mass of the sphere at the bottom of the incline?
sqrt(2gh)
