The equation of motion of a particle is s(t)=t^3−3t, where s is in meters and t is in seconds. Assume that t≥0.

Question

Find the acceleration when velocity is zero.

Answer 1

s(t) = t³ − 3t

The velocity is the 1st derivative: v(t) = s'(t) = 3t² - 3

Acceleration is the 2nd derivative: a(t) = s"(t) = 6t

The velocity is 0 when t = 1, at which time the acceleration is 6