Question

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.

Answer 1

Given, velocity of first car, v₁ = 15 km/h

And velocity of second car, v₂ = 45 km/h

Since masses are same, kinetic energy is directly proportional to the square of the velocity (Kav₂)

Hence, ratio of their kinetic energies is:

`therefore k_1/k_2 = v_1^2/v_2^2`

`therefore k_1/k_2 =15^2/45^2`

`therefore k_1/k_2 = (cancel(15)^1 xx cancel(15)^1)/(cancel(45)_3 xx cancel(45)_3)`

`therefore k_1/k_2 = 1/(3 xx 3)`

`therefore k_1/k_2 = 1/9`

∴ k₁ / k₂ = 1 : 9