The equation of motion of a particle is s = t3 − 3t, s is in meters and t is in seconds. (Assume t =/> 0)

1- Find the velocity and acceleration as functions of t.

2- Find the acceleration after 4 s.

3- Find the acceleration when the velocity is 0.

1. the velocity v(t) = ds/dt = 3t^2 - 3

acceleration a(t) = dv/dt = 6*t

2. a(4)=6*4=24 m/s^2

3. v = 0 = 3t^2 - 3

3t^2=3t^2 = 3/3 t^2 = 1 t=+1 t = - 1 has no meaning. at t=1 the acceleration is a(1) = 6*1 = 6 m/s^2

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