Question

A car is running at a speed of 15 km/h while another car of the same mass is moving at a speed of 30 km/hr. Find the ratio of their kinetic energy.

Answer 1

Step 1, Given data

Speed of the first car = $v_1=15$ km/h

Speed of the second car = $v_2=30$ km/h

Let the mass of both the cars be M

Step 2, Finding the ratio of kinetic energy

The kinetic energy of the first car = ${KE}_1=\frac{1}{2}M{v_1}^2$

Putting all the values

${KE}_1=\frac{1}{2}\times M\times {15}^2=\frac{225M}{2}$

The kinetic energy of the second car = ${KE}_2=\frac{1}{2}M{v_2}^2$

Putting all the values

${KE}_2=\frac{1}{2}\times M\times {30}^2=\frac{900M}{2}$

Now ratio

$\frac{K{E}_1}{K{E}_2}=\frac{\frac{225M}{2}}{\frac{900M}{2}}=\frac{1}{4}$

Hence the ratio of the kinetic energy is 1 : 4