A particle moves such that dV/dt = -a * sqrt(V), where a is a positive constant and the initial velocity is V0. Find the time at which the particle comes to rest.

2*sqrt(V0)/a
sqrt(V0)/a
2*a*sqrt(V0)
a*sqrt(V0)

Correct answer: 2*sqrt(V0)/a

Solution

Separating: V^(-1/2) dV = -a dt. Integrating: 2*sqrt(V) = -a*t + C. At t=0, V=V0: C=2*sqrt(V0). At V=0: t = 2*sqrt(V0)/a.

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