Solve the following question.

Question

If 𝑠(𝑡)=1/3𝑡^3−2𝑡^2−5t+4 for 𝑡 ≥ 0, find the acceleration of the object when its velocity is zero.

Answer 1

s(t) = (1/3)t³ - 2t² - 5t + 4

s'(t) = v(t) = velocity = t² - 4t - 5 = (t - 5)(t + 1)

v(t) = 0 when t = 5 or t = -1 (Since t > 0, t = 5)

s"(t) = a(t) = acceleration = 2t - 4

a(5) = 6