Given, $\quad x(t)=x_{0}\left(1-e^{-\gamma t}\right)$

$v(t)=\frac{d x(t)}{d t}=x_{0} \gamma e^{-\gamma t}$

$a(t)=\frac{d v(t)}{d t}=-x_{0} \gamma^{2} e^{-\gamma t}$

$(a)$ When $t=0 ; x(t)=x_{0}\left(1-e^{-0}\right)=x_{0}(1-1)=0$

$v(t)=x_{0} \gamma e^{-0}=x_{0} \gamma(1)=\gamma x_{0}$

$(b)$ $x(t)$ is maximum when $\mathrm{t}=\infty$

$[x(t)]_{\max }=x_{0}(1-0)=x_{0}$

$x(t)$ is minimum when $\mathrm{t}=0$

$[x(t)]_{\min }=0$

$v(t)$ is maximum when $t=0 ; v(0)=x_{0} \gamma$

$v(t)$ is minimum when $t=\infty ; v(\infty)=0$

$a(t)$ is maximum when $t=\infty ; a(\infty)=0$

$a(t)$ is minimum when $\mathrm{t}=0 ; a(0)=-x_{0} \gamma^{2}$