A body of mass 1 kg begins to move under the action of a time dependent force F → = t i ^ + 3 t 2 j ^ N , where i ^ and j ^ are the unit vectors along x and y axis. The power developed by above force, at the time t = 2 s , will be _______ W .

Step-by-step solution

Given, F → = t i ^ + 3 t 2 j ^   N and m = 1   kg Now, we can write from Newton's second law, F → = m a → = m d v → d t Then, d v → = t i ^ + 3 t 2 j ^ d t Integrating the above, ∫ 0 v d v → = ∫ 0 t t i ^ + 3 t 2 j ^ d t ⇒ v → = t 2 2 i ^ + t 3 j ^ Now, power developed by the force is P = F → · v → = t i ^ + 3 t 2 j ^ · t 2 2 i ^ + t 3 j ^ = t 3 2 + 3 t 5 At t = 2   s , power is P = 2 3 2 + 3 2 5 = 4 + 3 × 32 =