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Asked in NEET 2015 · Motion under constant power
Given: constant power k, particle of mass m starting from rest.
Idea: constant power means the work grows linearly with time, so the speed follows from the work-energy theorem.
W=kt=1/2mv², so v=√(2kt)/m.
a=(dv)/(dt)=1/2√(2k)/m t^-1/2=√k/(2m) t^-1/2.
F=ma=m√k/(2m) t^-1/2.
F=√(mk)/2 t^-1/2.
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