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 ?

Options

A.
B. .
C. .
D. .

Answer

A

Explanation

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