Question

The velocity-displacement graph of a particle is as shown in the figure

Which of the following graphs correctly represents the variation of acceleration with displacement?

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

Answer 2

For the given velocity – displacement graph,

Intercept = $v_{0}$and slope $= - \frac{V_{0}}{x_{0}}$

Thus, the equations of given lien of velocity-displacement graph is

$v = - \frac{v_{0}}{x_{0}}x + v_{0}$

Accelerations, $a = \frac{dv}{dt} = \frac{dv}{dx}\frac{dx}{dt} = \frac{dv}{dx}v$

$\because \frac{dv}{dx} = - \frac{v_{0}}{x_{0}}$

$\therefore$ $a = - \frac{v_{0}}{x_{0}}\left( - \frac{v_{0}}{x_{0}}x + v_{0} \right)$ (Using (i))

$= \frac{v_{0}^{2}}{x_{0}^{2}}x0\frac{v_{0}^{2}}{x_{0}}$

In is a straight line with positions slope and a negative intercept.

The variation of a with x is as shown in the figure.