Give examples of a one-dimensional motion where
(a) the particle moving along positive x-direction comes to rest periodically and forward.
(b) the particle moving along positive x-direction comes to rest periodically and moves backward..

Explanation

The motion must be linked with periodic motion represented by sine or cosine function.
(a) Let x(t)=`-sin t`
`therefore v=(dx)/(dt)=1- cos t`
and `a=(dv)/(dt)=sin t`
When t=0, x=0
when `t=pi, x=pi-sin pi =pi gt 0`
(b) Let x(t)=`cos t`
`v=(dx)/(dt)=cos t`
As x and v are involving `sin t` and `cos t`, hence, these equations represent periodic motion.