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

Step 1: Given Data:-

Mass of object $=m$

The initial velocity of the object $=v$

The final velocity of the object $=0$

Step 2: Calculating Work Done

We know that,

The work done is equal to the change in the kinetic energy of an object.

Then,

$$\begin{gathered} W=△K.E \\ W=FinalKineticEnergy-InitialKineticEnergy \\ W={K.E}_f{-K.E}_i \\ W=\frac{1}{2}m{\left(0\right)}^2-\frac{1}{2}m{\left(v\right)}^2 \\ W=0-\frac{1}{2}m{v}^2 \\ W=-\frac{1}{2}m{v}^2 \end{gathered}$$

The magnitude of work done is $\frac{1}{2}m{v}^2$

Hence, $\frac{1}{2}m{v}^2$ work should be done on the object in order to bring the object to rest.