A 1 kg body starts from rest under the time-dependent force F ⃗ \vec{F} F =(t î+3t² ĵ) N. Find the instantaneous power at t=2 s in watts.
Physics · Work , Power and Energy · Power
JEE Mains 2023

Question

A 1 kg body starts from rest under the time-dependent force F ⃗ \vec{F} F =(t î+3t² ĵ) N. Find the instantaneous power at t=2 s in watts.

G1 Physics · Accepted Answer

For m=1 kg, acceleration equals F⃗. Starting from rest, v⃗=∫F⃗dt=(t²/2)î+t³ĵ. At t=2, v⃗=2î+8ĵ and F⃗=2î+12ĵ. Power F⃗·v⃗=4+96=100 W.