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?

To bring an object of mass (m) and constant velocity (v) to rest, we need to reduce its kinetic energy to zero.

The work (W) done on an object is equal to the change in its kinetic energy. The kinetic energy (KE) of an object moving with velocity (v) is given by:

KE = 1/2 mv²

When the object is brought to rest, its final kinetic energy (KE_final) will be zero.

The initial kinetic energy (KE_initial) of the object moving with velocity (v) is 1/2 mv²).

Therefore, the work done to bring the object to rest is:

W = KE_final – KE_initial = 0 – 1/2} m v² = – 1/2 m v²

Hence, to bring an object of mass (m) moving with constant velocity (v) to rest, a total amount of work equal to ( -1/2 m v²) needs to be done on the object. The negative sign indicates that work is done against the object’s motion to reduce its kinetic energy to zero.