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

a(t)=_______

(b) Find the acceleration after 4 s.

_______ m/s²

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

_______ m/s²

Answer 1

Simon,

Velocity is the derivative of position.

Acceleration is the derivative of velocity, so it will be the second derivative of position.