Question

If the speed of the body is halved, what will be the change in its $K.E.?$

Answer 1

Step 1:Given data

The velocity of the body is halved, then it is given by

New velocity,$v\text{'}=\frac{v}{2}$

Step 2: Finding KE

The formula of the kinetic energy.

$\mathit{K}\mathit{E}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathit{m}{\mathit{v}}^{\mathbf{2}}$

New KE when velocity becomes half is,

$$\begin{gathered} \mathit{K}\mathit{E}\mathbf{\text{'}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathit{m}{\left(\frac{v}{2}\right)}^{\mathbf{2}} \\ \mathbf{=}\frac{\mathbf{1}}{\mathbf{4}}\mathbf{\times }\frac{\mathbf{1}}{\mathbf{2}}\mathit{m}{\mathit{v}}^{\mathbf{2}} \\ \mathit{K}\mathit{E}\mathbf{\text{'}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{4}}\mathit{K}\mathit{E} \end{gathered}$$

When the speed of the body is halved, the kinetic energy becomes one-fourth of its initial kinetic energy.