The kinetic energy of an object of mass m, moving with a velocity of 5 m/s is 25 J. What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times?

Given, velocity of the object(v) = 5 m/s and mass of the object = m

kinetic energy of the object( \( E_k \) ) = 25 J

We know that, \( E_k \ = \ \frac{mv^2}{2} \)

(i) So, if the velocity is doubled, kinetic energy will become 4 times its initial value, i.e., \( E_k = 4 × 25 \ = \ 100 \ J \)

\(\therefore \) kinetic energy is directly proportional to square of velocity.

(ii) Similarly, if velocity is increased three times then kinetic energy will become 9 times of its initial, i.e., \( E_k \ = \ 25 × 9 \ = \ 225 \ J \)