Question

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 1

An object with mass 'm' moving with a velocity 'v' has kinetic energy $\frac{1}{2}m{v}^2$
In order to bring the object to rest, its velocity has to be reduced to zero. This means it's kinetic energy has to be drained off. An external force has to absorb energy from the object, i.e. do negative work equal to its kinetic energy, or
$W=-\frac{1}{2}m{v}^2$