A stone is dropped from the edge of a cliff. Which of the following graphs best represents the stone's kinetic energy KE as a function of time t?

A block of mass m is placed on the frictionless inclined plane with an incline angle θ. The block is just in a contact with a free end on an unstretched spring with a spring constant k. If the block is released from rest, what is the maximum compression in the spring?

A 4.0 N force is used to accelerate a 2.0 kilogram block from rest to a velocity of 6.0 m/s. If the force was applied over a distance of 15 meters, the coefficient of kinetic friction between the block and the surface is most nearly

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

The position of an object is given by the equation x = 3.0 t2 + 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?

The position of a toy locomotive moving on a straight track along the x-axis is given by the equation x = t³ – 6t² + 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

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 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

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?

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?

A bar is pivoted about one end and is initially at rest in a vertical position. The bar is displaced slightly and as it falls it makes an angle 𝜽 with the vertical at any given time. Which of the following graphs best represents the bar’s angular acceleration 𝜶 as a function of angle 𝜽 ?

A specially designed spring is stretched from equilibrium to the distances x given in the table above, and the restoring force F is measured and recorded in each case. What is the potential energy of the spring when it is stretched 3 m from equilibrium?

The graph above shows the force acting on an object as a function of time. The change in momentum of the object from time 0 to t is

Which of the following is/ are characteristics of simple harmonic motion?

I. The acceleration is constant .

II. The restoring force is proportional to the displacement.

III. The frequency is independent of the amplitude.

A simple pendulum swings about the vertical equilibrium position with a maximum angular displacement of 5^o and period T. If the same pendulum is given a maximum angular displacement of 10^o, then which of the following best gives the period of the oscillations?

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?

A 10-kg ghost is constrained to move along the x-axis. The potential energy U of the ghost is given as a function of its position by the function below. Calculate the force on the ghost at x = 3 m.

The speed v of an automobile moving on a straight road is given in meters per second as a function of time t in seconds by the following equation:

v(t) = 4 + 2t ³

What is the acceleration of the automobile at t = 2 s ?

A particle moves in the xy-plane with coordinates given by x=Acosωt and y=Asinωt, where A=1.5 meters and ω=2.0 radians per second.

What is the magnitude of the particle's acceleration?

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?

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 net force on the ball at point P?

To stretch a certain nonlinear spring by an amount x requires a force F given by

F = 40x – 6x² ,

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?

A block slides from rest with negligible friction down the track above, descending a vertical height of 5.0 m to point P at the bottom. It then slides on the horizontal surface. The coefficient of friction between the block and the horizontal surface is 0.20. How far does the block slide on the horizontal surface before it comes to rest?

Three objects are located along the x-axis as shown above. The center of mass of the objects is at x = ___.

The graph above shows the force on an object of mass M as a function of time. For the time interval 0 s to 4 s, the total change in the momentum of the object is _____.

A moon of mass m orbits a planet of mass 49m in an elliptical orbit as shown above. When the moon is at point A, its distance from the center of the planet is r_A and its speed is v₀. When the moon is at point B, its speed is 5v₀.

When the moon is at point A, the distance from the moon to the center of mass of the planet-moon system is most nearly ____.

A disk is free to rotate about an axis perpendicular to the disk through its center. If the disk starts from rest and accelerates uniformly at the rate of 3 radians/s² for 4 seconds, its angular displacement during this time is ___.

A wheel of 0.5-meter radius rolls without slipping on a horizontal surface. The axle of the wheel advances at constant velocity, moving a distance of 20 meters in 5 seconds. The angular speed of the wheel about its point of contact on the surface is ___.

A simple pendulum consists of a 1.0-kilogram brass bob on a string about 1.0 meter long. It has a period of 2.0 seconds. The pendulum would have a period of 1.0 second if the ____.

A ball is tossed straight up from the surface of a small, spherical asteroid with no atmosphere. The ball rises to a height equal to the asteroid's radius and then falls straight down toward the surface of the asteroid. The acceleration of the ball at the top of its path is ___. 

A newly discovered planet is found to have twice the radius and five times the mass of Earth. If the acceleration of gravity at the surface of Earth is g, the acceleration of gravity at the surface of the new planet is __.

A comet moves in the Sun’s gravitational field, following the path shown above. What happens to its angular momentum as it moves from point X to point Y ?

The elliptical orbit of a comet is shown above. Positions 1 and 2 are, respectively, the farthest and nearest positions to the Sun, and at position 1 the distance from the comet to the Sun is 10 times that at position 2. At position 2, the comet’s kinetic energy is ___.

An unstretched ideal spring hangs vertically from a fixed support. A 0.4 kg object is then attached to the lower end of the spring. The object is pulled down to a distance of 0.35 m below the unstretched position and released from rest at time t = 0 . A graph of the subsequent vertical position y of the lower end of the spring as a function of t is given above, where y = 0 when the spring was initially unstretched. At which of the following times is the upward velocity of the object the greatest?