A 2 kg particle starts from rest under the action of the time-dependent force F = 2t î+6t² ĵ newtons. If the instantaneous power delivered by this force at t = 2 s is N watts, find N.
Physics · Work , Power and Energy · Power
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Question

A 2 kg particle starts from rest under the action of the time-dependent force F = 2t î+6t² ĵ newtons. If the instantaneous power delivered by this force at t = 2 s is N watts, find N.

G1 Physics · Accepted Answer

The acceleration is a = F ÷ m = t î+3t² ĵ. The particle starts from rest, so its velocity at time t is v = ∫₀ᵗ a dt = (t² ÷ 2)î+t³ĵ. At t = 2 s: v = 2î+8ĵ m·s⁻¹. The force at t = 2 s is F = 4î+24ĵ N. Instantaneous power is P = F·v = 4×2+24×8 = 8+192 = 200 W. Therefore N = 200.