Question

The given graph shows the variation of velocity with displacement. Which one of the graphs given below correctly represents the variation of acceleration with displacement?

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

Given line have positive intercept but negative slope. So its equation can be written as
$v = - mx + v_0 \,...(i) [ $ where $ m = \tan\,\theta = \frac{v_0}{x_0}]$
By differentiating with respect to time we get
$\frac{dv}{dt} = - m \frac{dx}{dt} = - mv$
Now substituting the value of $v$ from eq. (i) we get
$\frac{dv}{dt} = -m[-mx + v_0]$
$ = m^2 x - mv_0$
$\therefore a = m^2 x - mv_0$
i.e. the graph between $a$ and $x$ should have positive slope but negative intercept on $a$-axis.