Give ezamles of a one-dimenssionl motion wher
(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

In on edimensional motion, the displacement of the particle in periokic motion must be linked with sine or cosing function. The particle will be moving alon + ive x-direction only if ` t gt sin t`. Hence,
` x (t) =- t - sin t`.
Velocity, ` v (t) = (dx0 (t) 0/(dt) =1- cso t` and acceleration, `a (t) = (dv)/(dt) = sint`
`v (t) =0, when ` t= 0 or 2 pi and a (t) =0`.
Whem ` t = pi`, dospacement, `x (t) = pi - sin pi = pi (poritive)`
Whem ` t = 2 pi`, dospacement, `x (t) = pi - sin pi = pi (poritive)`
(b) In one dimensional motion, where a particle moving along positive x-direction comes to rest preiodically an dmoves bachward can be represented by ` x (t) = sin t`.
Here, ` v = (dx)/(dt) = cos t`
acceleration, `a = (dv)/(dt) =- sin t`
When ` t=0, x =0, v =positive, a =0`
When ` t= pi //2`, x= + ive, v=0, a=- ve
When ` t= -pi, x=0, v=- ve, a=0`
When ` t= 3 pi //2, x =- ive, v=- 0, a= + ive`
When ` 1= 2 pi , x =0 , v= + ve , a=0`.