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Answer :
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., \( E_k \ = \ 25 × 9 \ = \ 225 \ J \)