Graph of velocity versus displacement of a particle moving in a straight line is as shown in figure.
The acceleration of the particle is.

Options

A. constant
B. increases linearly with `x`
C. increases parabolically with `x`
D. none of these

Answer

B

Explanation

From the graph, velocity-displacement equation can be written as :
`v = v_0 + alpha x` ….(1)
Here `v_0` and `alpha` are positive constants.
Differentiating (1) with respect to `x` we get
`(dv)/(dx) = alpha = constant`
Acceleration of the particle can be written as
`a = v. (dv)/(dx) = (v_0 + alpha x) . alpha`
`alpha- x` equation is a linear equation. Thus acceleration increases linearly with `x`.