An object of mass, m is moving with a constant velocity, v. how much work should be done on the object in order to bring the object to rest?

Answer:

The kinetic energy of an object of mass m, moving with a velocity, v is given by the expression,
K.E = 1/2 mv²

Explanation

In order to bring it to rest, its velocity has to be decreased to zero, and in order to achieve that, the kinetic energy has to be drained off and sent somewhere else. An external force has to absorb energy from the object, i.e. do negative work on it, equal to its kinetic energy, or -1/2 mv².

Kinetic energy

Kinetic energy is the measure of the work an object can do by virtue of its motion. The total work that is done on a system is equivalent to the change in kinetic energy. Therefore, this statement is equated as follows:

W_net = ΔK

This equation is known as the work-energy theorem and has large applications even if the forces applied to vary in magnitude and direction.