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

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Infinity Learn · Accepted Answer

Power k $$=$$ F.v $$=$$ (ma)v$$ $$=$$ mdvdt v $$=$$ mvdvdtRearranging we get, vdv $$=$$ kmdtIntegrating both side,∫$$0vvdv$$ $$=$$ km∫$$0tdt$$     ⇒ $$v22$$ $$=$$ kmt⇒v $$=$$ $$2$$ $$ktm---------------(i)Force$$ acting on particle F $$=$$ $$mdvdt------(ii)Differentiating$$ equation $$(i) w.r.t timedvdt $$=$$ (2km)dt-12d$$ $$=$$ $$(2km)12t-12$$ $$=$$ $$(k2m)t-12Substituting$$ the value of dvdt in equation $$(ii) we getF $$=$$ mdvdt $$=$$ $$m(k2m)t-12$$ $$=$$ (mk2t-12)

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

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