Question

Give examples of a one-dimensional motion where

A. The particle moving along positive x-direction comes to rest periodically and moves forward.

Answer 1

When we are writing an equation belonging to periodic nature it include sine or cosine function.

So Assume, $x=t-sint$

$sint=t-\frac{t^3}{3!}+\frac{t^5}{5!}-\frac{t^7}{7!}$

sint<t

$x\left(t\right)>0forallt>0,x>0$, $x>0$

$\frac{dx}{dt}=v\left(t\right)=1-cost$

As$-1<costt<1$

$v_{max}=2$

$v_{min}=0$

So, here particle is moving forward as $x\left(t\right)>0$ for all $t>0$ and it comes periodically at rest.