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

$\frac{dv}{dt}=-m[-mx+v_0]$

$=m^{2}x-m{v}_0$

$\therefore a=m^{2}x-m{v}_0$

i.e. the graph between $a$ and $x$ should have positive slope but negative intercept on $a$-axis.