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

(a) If the position of a particle is given by \( x = 20t - 5t^3 \), where \( x \) is in meters and \( t \) is in seconds, when, if ever, is the particle’s velocity zero? (b) When is its acceleration a zero? (c) For what time range (positive or negative) is \( a \) negative? (d) Positive? (e) Graph \( x(t) \), \( v(t) \), and \( a(t) \).