Question

If a particle’s speed increases by a factor of 3, by what factor does its kinetic energy change?

Short answer

It will change by a factor of 9

Step-by-step solution

Given information

Velocity is changed by a factor of 3

Explanation

Kinetic energy is given by

$KE=\frac{1}{2}m{v}^2$

Lets say velocity is changed to v'=3v, then

kinetic energy will become

$KE\text{'}=\frac{1}{2}mv{\text{'}}^2=\frac{1}{2}m{\left(3v\right)}^2=\frac{9}{2}m{v}^2$

Now find ratio
$\frac{KE\text{'}}{KE}=\frac{{\displaystyle \frac{9}{2}}m{v}^2}{{\displaystyle \frac{1}{2}}m{v}^2}=9$

It will increase by a factor of 9.