Question

An object of mass $\mathrm{m}$ 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$=\mathrm{m}$

Initial velocity, $v_i=v$

Final velocity, $v_f=0$

Step 2: Calculate the work required

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

The change in kinetic energy $k$ is calculated below:

$$\begin{gathered} k=\frac{1}{2}\mathrm{m}{v_f}^2-\frac{1}{2}\mathrm{m}{v_i}^2 \\ k=0-\frac{1}{2}\mathrm{m}{{\mathrm{v}}_{\mathrm{i}}}^2\left[{\mathrm{v}}_{\mathrm{f}}=0,{\mathrm{v}}_{\mathrm{i}}=\mathrm{v}\right] \\ k=-\frac{1}{2}\mathrm{m}{{\mathrm{v}}_{}}^2 \end{gathered}$$

Hence, the work required to stop the object is $-\frac{1}{2}\mathrm{m}{{\mathrm{v}}_{}}^2$.