Find the acceleration when the velocity is 0.

Question

The equation of motion of a particle is s = t³ − 12t, where s is in meters and t is in seconds. (Assume t ≥ 0.)

(a) Find the velocity and acceleration as functions of t.

v(t)= 3t²-12

a(t)= 6t

(b) Find the acceleration after 4 s.

24 m/s²

(c) Find the acceleration when the velocity is 0.

_______ m/s²

Answer 1

Here we set v(t) = 0 and solve for t, then we plug t into a(t):

0 = 3t² - 12

4 = t²

t = 2 seconds

a(2) = 6(2) = 12 m/s²