The equation of motion of a particle is s = t^3 − 12t, where s is in meters and t is in seconds. (Assume t ≥ 0)

Question

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

v(t)=

a(t)=

(b)Find the acceleration after 9 s.

________m/s^2

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

________m/s^2

Answer 1

(a)

Velocity is the derivative of position:

v(t) = s'(t) = 3*t^2 - 12

and acceleration is the derivative of velocity:

a(t) = 6*t

(b)

acceleration at t = 9s is a(9) = 6*9 = 54 m/s2

(c)

if velocity is zero:

v(t) = 3*t^2-12 = 0

t^2 = 4

t = 2 s

and therefore,

a(2) = 6*2 = 12 m/s2