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

1. The energy possessed by an object by virtue of its motion is called Kinetic Energy.
2. The kinetic energy of the given object of mass $m$, moving with a velocity, $v$ is given by the expression, $K.E=\frac{1}{2}m{v}^2$
3. 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 transferred somewhere else.
4. An external force has to absorb energy from the object, i.e., we have to do negative work on it, equal to its kinetic energy, or $-\frac{1}{2}m{v}^2$.
5. The total work that is done on a system is equivalent to the change in kinetic energy. Therefore, this statement is equated as follows: $W_{net}=\Delta K$.
6. Hence, $W_{net}=\Delta K$much work should be done on the object in order to bring the object to rest.