A body of mass m = 10 − 2 kg is moving in a medium and experiences a frictional force F = − k v 2 . Its initial speed is v 0 = 10 m s − 1 . After 10 s its kinetic energy is 1 8 m v 0 2 , then value of k will be:-

Step-by-step solution

After 10   sec, 1 2 m v 2 = 1 8 m v 0 2 ⇒ v = v 0 2 = 5   m   s - 1 Acceleration, a = − k v 2 m ⇒   d v d t = − k v 2 m ⇒   ∫ 10 5 d v v 2 = − k m   ∫ 0 10 d t - 1 5 + 1 10 = - k 10 - 2 × 10 k = 10 − 4   kg   m - 1