An object has a mass, M, and a velocity, V.

What happens to the object's kinetic energy if its velocity is doubled?

A bungie jumper of mass is attached to a bungie with a constant of . The unstretched length of the bungie is . What is the maxmimum velocity of the jumper?

An object of mass moves with velocity . How fast must an object of mass move in order to have the same kinetic energy of the object of mass ?

Two objects, one of mass, , and the other of mass, , are traveling at constant velocity along a frictionless surface. The lighter object travels at , while the heavier travels at . An opposing horizontal force acts upon both objects equally, and brings them to rest. Which object takes longer to slow down, and why?

A ball with a mass of 3 kilograms is uniformly accelerated from rest and travels 110 meters in 6 seconds. What is its final kinetic energy in Joules after 6 seconds?

How much greater is the energy of a car crash at than .

In an investigation into energy, a student compresses a spring a distance of from its neutral length. She then puts a cart against the end of the spring and releases both the spring and the cart. She measures the velocity of the cart after the spring has returned to its neutral length and finds it to be . She then repeats the experiment, but this time compresses the spring a distance of before releasing the spring and the cart. What would the cart's velocity be in the second experiment?

Consider the following system:

Two spherical masses, A and B, are attached to the end of a rigid rod with length l. The rod is attached to a fixed point, p, which is at the midpoint between the masses and is at a height, h, above the ground. The rod spins around the fixed point in a vertical circle that is traced in grey. is the angle at which the rod makes with the horizontal at any given time ( in the figure).

The rod is initially at rest in its horizontal position. of work were applied toward rotating the rod. When the rod passes through its horizontal position now, what is the instantaneous linear velocity of mass A?

Neglect air resistance and any internal friction forces.

Moment of inertia of hollow sphere:

A kickball of mass and radius is on top of a hill of height , at the edge of a straight incline to the bottom. Suppose the ball was just barely pushed over the edge. Calculate the ball's velocity at the bottom of the hill. It may be assumed that the ball is essentially hollow. Ignore any losses due to friction, as well as any velocity from the initial push.

Moment of inertia of a ring:

A bicycle wheel has a mass of and a radius of . Determine the total kinetic energy of the wheel if the bicycle is moving at . The wheel may be approximated as a hollow ring.