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

### Step-by-Step Text Solution

#### Part (a): Example of One-Dimensional Motion Where the Particle Comes to Rest Periodically and Moves Forward

1. **Define the Position Function**:
We can define the position of the particle as a function of time, \( x(t) = t - \sin(t) \).

2. **Find the Velocity**:
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