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 :
Answer & explanation
Correct answer: option 4
P = Fv = v.ma
K = mv \(\frac{dv}{dt}\)
On integrating : v = \(\sqrt{\frac{2kt}{m}}\)
a = \(\frac{dv}{dt}\) = \(\sqrt{\frac{2kt}{m}} \frac{1}{2\sqrt{t}}\)
F = \(\sqrt{\frac{mk}{2t}}\)