Dynamics_Part5

Dynamics_Part5 - Problem Set 1 Problem 5 Problem The...

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Problem Set 1: Problem 5. Problem: The acceleration of a particle is a = λ v , where λ is a constant. At time t = 0 the particle is located at x = 0 and its velocity is v = V . Also, when its position is x = f the particle’s velocity is v = 1 4 V . (a) Determine the constant λ . (b) At what time τ does the particle come to rest? Solution: Since we know the acceleration as a function of velocity, the obvious first step in solving this problem is to begin with the differential equation relating acceleration and velocity, viz., a = v dv dx = a dx = v dv (a) For the given acceleration, we have λ v dx = v dv = dx = 1 λ v dv Then, integrating, we have 8 x o dx = 1 λ 8 v V v dv = x = 2 3 λ v 3 / 2 e e e e v = v v = V Thus, the particle’s position as a function of its velocity is x = 2 3 λ p v 3 / 2 V 3 / 2 Q We can now determine the value of
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