The velocity-displacement graph of a particle is shown in the figure.

(a) Write the relation between v and x.
(b) Obtain the relation between acceleration and displacement and plot it.


Hint: Appy acceleration, a = vdvdx.
Step 1: Find the relation between v and x. 

Given, initial velocity = v0
 For the graph tanθ = v0x0 = v0vx                     ...(I)
where, v is velocity and x is the displacement at any instant of time t.

Step 2: Find velocity as a function of displacement using the above relation.

 From Eq. (i) v0v=v0x0xv =v0x0x+v0

Step 3: Find acceleration by using the relation acceleration, a = vdvdx.

 Acceleration a=vdvdx=-v0x0x + v0×-v0x0                       =v0x0v0x0x+v0                       =v02x02xv02x0.

Step 4: Plot the graph of a vs x.

The graph of a versus x is

 

.