A particle executes the motion described by `x (t)=x_(0) (1-e^(-gamma t)) , t gt =0, x_0 gt 0`.
(a) Where does the particle start and with what velocity ?
(b) Find maximum and minimum values of ` x (t) , a (t)`. Show that ` x (t) and a (t)` increase with time and ` v(t)` decreases with time.

Explanation

To solve the problem step by step, we will analyze the motion of the particle described by the equation \( x(t) = x_0 (1 - e^{-\gamma t}) \).

### Part (a): Initial Position and Velocity

1. **Initial Position**:
- At \( t = 0 \):
\[
x(0) = x_0 (1 - e^{-\gamma \cdot 0}) = x_0 (1 - 1) = 0
...