A car is running at a speed of 15 km h^-1 while another similar car is moving at a speed of 45 km h^-1. Find the ratio of their kinetic energies.

We know that,

$KE =\dfrac{1}{2} \times m \times v^2 \\[0.5em]$

Hence, KE α v²

So we get,

$\dfrac{KE$1}{KE2} = \dfrac{v1^2}{v2^2} \\[0.5em] \dfrac{KE1}{KE2} = (\dfrac{15}{45})^2 \\[0.5em] \dfrac{KE1}{KE2} = (\dfrac{1}{3})^2 \\[0.5em] \Rightarrow \dfrac{KE1}{KE2} = (\dfrac{1}{9}) \\[0.5em]