Walker, Halliday & Resnick — Motion Along a Straight Line: Problem 20

20 (a) If the position of a particle is given by \(x = 25t - 6.0t^3\), where \(x\) is in meters and \(t\) is in seconds, when, if ever, is the particle’s velocity \(v\) zero? (b) When is its acceleration \(a\) zero? For what time range (positive or negative) is \(a\) (c) negative and (d) positive? (e) Graph \(x(t)\), \(v(t)\), and \(a(t)\).