Question

Velocity (v) versus desplacement (x) plot of a body moving along a straight line is as shown in the graph. The corresponding plot of acceleration (a) as a function of displacement (x) is

Answer 1

From the given graph equation for velocity `v=kx` on differentiation.
`(dv)/(dt)=kv` .(i)
`(dv)/(dt)=k(kx)=k^(2)x`,
`a=k^(2)x` and `v=-kx+v_(0)`
on differentiation `(dv)/(dt)=-kv=-k(-kx+v_(0))`
So, according to the eq. (ii) the shape of a-x graph is as below