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?

An object with mass 'm' moving with constant velocity 'v' has kinetic energy of,

  $K.E=\frac{1}{2}m{v}^2$
According to work - energy theorem, the work done is given by the change in kinetic energy.

$W=K_f-K_i$   

$W=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2$

So, if the final kinetic energy is zero, i.e., K.E_f = 0 since the object comes to rest, then the work done on the object in order to bring it to rest will be equal to,

$W=-K.E_i = -\frac{1}{2}m{v}^2$