Graph between velocity and displacement is shown in the following figure:

Which of the following graphes represents the correct variation of acceleration with displacement

Options

A.
B.
C.
D. none

Answer

a

Explanation

Velocity in terms of displacement (x) can be written from the graph as follows:
`rArr v=v_(0)-(v_(0))/(x_(0))((dx)/(dt))`
`rArr a=-(v_(0))/(x_(0))(v)`
Substituting v in above equation we get the following:
`rArr a=-(v_(0))/(x_(0))(v_(0)-(v_(0))/(x_(0))x)`
`rArr a=(v_(0)^(2))/(x_(0)^(2))x-(v_(0)^(2))/(x_(0))`