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 ?

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)

Tardigrade Admin · Accepted Answer

For the given velocity-displacement graph, intercept

= v_{0}

and slope

= - \frac{v _{0}}{x _{0}}

Thus, the equation of given line of velocity-displacementgraph is

v = \frac{v _{0}}{x _{0}} x + v_{0} \dots (i)

Acceleration,

a = \frac{d v}{d t} = \frac{d v}{d x} \frac{d x}{d t} = \frac{d v}{d x} v

∵ \frac{d v}{d x} = - \frac{v _{0}}{x _{0}}

∴ a = \frac{v _{0}}{x _{0}} (- \frac{v _{0}}{x _{0}} x + v_{0})

(Using

(i)

)

= \frac{v _{0}^{2}}{x _{0}^{2}} x - \frac{v _{0}^{2}}{x _{0}}

It is a straight line with positive slope and a negative intercept.
The variation of

a

with

x

is as shown in the above figure.

Q. 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 ?