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

When an object is moving with a constant velocity, its kinetic energy is given by the equation:

Kinetic Energy= $\frac 12​mv^2$

If you want to bring the object to rest, you need to remove all of its kinetic energy. The work done (W) is equal to the change in kinetic energy. In this case, the change in kinetic energy is equal to the initial kinetic energy (when the object is moving with velocity v).
So, the work done (W) to bring the object to rest is given by:

W= Change in Kinetic Energy = Final Kinetic Energy − Initial Kinetic Energy

Since the final kinetic energy is zero (the object is at rest), and the initial kinetic energy is $\frac 12​mv^2$, the work done is:

$W=0−\frac 12​mv^2$

Therefore, the work done to bring the object to rest is $-\frac 12mv^2$. The negative sign indicates that work is done against the motion of the object, removing its kinetic energy.