Question

If the velocity of an object is doubled, what is the change in its K.E.?

Answer 1

Step 1:Given

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

Step 2:Finding change in KE

Kinetic energy can be expressed as

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

substituting $\mathit{v}\mathbf{\text{'}}\mathbf{=}\mathbf{2}\mathit{v}$ in the formula of kinetic energy

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

$\mathit{K}\mathit{E}\mathbf{\text{'}}\mathbf{=}\mathbf{4}\mathbf{\times }\frac{\mathbf{1}}{\mathbf{2}}\mathit{m}{\mathit{v}}^{\mathbf{2}}$

$\mathit{K}\mathit{E}\mathbf{\text{'}}\mathbf{=}\mathbf{2}\mathit{K}\mathit{E}$

Hence, when velocity is doubled, kinetic energy becomes 4 times.