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

Give examples of a one-dimensional motion where (a) The particle movi

1.	Give examples of a one-dimensional motion where (a) The particle moving along positive x-direction comes to rest periodically and moves forward.(b) The particle moving along positive x-direction comes to rest periodically and moves backward.
Answer» SOLUTION :When we are writing an equation BELONGING to periodic nature it include SINE or cosine function. (a) The particle will be moveing along positive X-direction only if `x(t) =1 - sin t` Velocity `v (t) = (dx(t))/(dt) =1 - cos t` Acceleration `a (t) = (dv)/(dt) = sin t ` When `t =0, x (t) =0` When `t = pi , x (t) = pi gt 0` When `t =0, x (t) = 2pi gt 0` (b) Equation can be represented by `x (t) = sin t ` `therefore v = (d)/(dt) x (t) = cos t ` As DISPLACEMENT and velocity includes sin t and cos t hence these equations represent periodic.