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Question:

A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest, the force on the particle at time t is

12√mk t1/2

√mk t1/2

√mk2t1/2

√2mk t1/2 -

Solution:

dW/dt = P ⇒ W = Pt ⇒ 1/2m(v22 - v12) = Pt ⇒ 1/2mv2 = Pt ⇒ v = √(2Pt/m) ⇒ a = dv/dt = √(2Pm) * (1/2)t-1/2 ⇒ F = ma = m√(2Pm) * (1/2)t-1/2 = √(mk)t-1/2