particle motion

Question

The position of a particle at time t seconds, t ≥0, is given by s(t)=t^2-sin(t) for 0≤ t ≤3,     where t is measured in seconds and s is measured in meters. Find the particle’s acceleration     each time the velocity is zero.

Answer 1

s'(t) = v(t) = 2t - 2cos t

Graph this to see that there is only one root, i.e. v(t)= 0 only for t = ,739085.

Use this value to compute a(t)= 2+ 2 sin t at this point.