Problem Set 1: Problem 4. Problem: A particle’s position is given by x = R [2( t/ τ ) 3 − ( t/ τ ) 4 ] ,whe re R and τ are characteristic length and time scales. Compute the time,t> 0 , at which the velocity is zero. What are the position and acceleration of the particle at this time? Solution: First, to simplify the differentiation process, rewrite the particle’s position as follows. x = R τ 4 J 2 τ t 3 − t 4 o The velocity of the particle is v = dx dt = R τ 4 J 6 τ t 2 − 4 t 3 o
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