A body hanging from a spring (fig.) is stretched 5 units beyond its rest position and released at time t =O to oscillate up and down. Its position at any later time (t) is

What are its velocity and acceleration at time t ?

We have

Position:  s = 5 cos t

velocity:  v = ds/dt=d/dt(5 cos t)=5(d/dt) cos t = -5 sin t

Acceleration: a= dv/dt=d/dt(-5 sin t)=5(d/dt)=-5 cos t