Explanation

(a) The $v - x$ equation from the given graph can be written as,
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v = \left( - \frac{v_{0}}{x_{0}} \right)\ x + v_{0}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ a = \frac{dv}{dt} = \left( - \frac{v_{0}}{x_{0}} \right)\frac{dx}{dt} = \left( - \frac{v_{0}}{x_{0}} \right)\ v$
Substituting $v$ from Eq. (i), we get
$\ \ \ \ \ \ \ \ \ \ a = \left( - \frac{v_{0}}{x_{0}} \right)\left\lbrack \left( - \frac{v_{0}}{x_{0}} \right)\ x + v_{0} \right\rbrack$
$\ \ \ \ \ \ \ \ \ a = \left( \frac{v_{0}}{x_{0}} \right)^{2}\ x - \frac{v_{0}^{2}}{x_{0}}$
Thus, $a - x$ graph is a straight line with positive slope and negative intercept.