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?

Options

A.
B.
C.
D.

Answer

A

Explanation

For the given velocity-displacement graph, intercept = `v_o` and slope = -`v_0/x_0`
Thus, the equation of given the velocity-displacement graph is
`v = -v_0/x_0 x + v_0` …(i)
Acceleration, `a = (dv)/(dt) = (dv)/(dx) (dx)/(dt) = (dv)/(dx) v`
since `= (dv)/(dx) = - v_0/x_0`
`therefore a = - v_0/x_0 (- v_0/x_0 x + v_0)` (Using (i))
`v_(0)^(2)/x_(0)^(2)x-v_(0)^(2)/x_(0)`
It is a straight line with positive slope and a negative intercept.
The variation of a x is as shown in the above figure.