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

When we are writing an equation belonging to periodic nature it will involve sine or cosine function
(a) The particle will be moving along positive x-direction only if `t gt sin t`
Hence, `x(t) = 1 - sint`
Velocity `v(t) = (dx(1))/(dt) = 1 - cos t`
Acceleration `a(t)= (dv)/(dt) = sint`
When `t = 0, x(t) = 0`
When `t = pi, x(t) = 0 pi gt 0`
When `t = 0, x(t) = 2 pi gt 0`
(b) Equation can be represented by
`x(t) = sint`
`v = (d)/(dt) x (t) = cos t`
As displacement and velocity is involving sint and cos t hence these equations represent periodic.