Question

What happens to the kinetic energy of an object if its velocity is doubled? Explain.

Answer 1

Kinetic energy can be expressed as

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

Where m is the mass, v is the initial velocity,

When the value of velocity becomes double of its initial value i.e. $v\text{'}=2v$

Substituting $v\text{'}=2v$ in the formula

$$\begin{gathered} KE\text{'}=\frac{1}{2}m{(v\text{'})}^2 \\ KE\text{'}=\frac{1}{2}m{\left(2\mathrm{v}\right)}^2 \end{gathered}$$

$KE\text{'}=4\times \frac{1}{2}m{v}^2$

$KE\text{'}=4\times KE$

Hence, when velocity is doubled, the kinetic energy becomes $\mathbf{4}$ times its initial value.