Question

The equation of motion of a particle is s = t3 â 27t, where s is in meters and t is in seconds. (assume t ⥠0.) (a) find the velocity and acceleration as functions of t.

Answer 1

The law of motion for the particle is

`S(t) = t^3 -27`
In order to find the velocity, we have to calculate the derivative of S(t):

`v= S'(t) = (d)/(dt) (t^3-27) =3t^2`
Similarly, to find the acceleration, we have to calculate the derivative of v(t):

`a(t)= v'(t) = (d)/(dt) (3t^2) = 6t`