Question

Velocity versus displacement graph of a particle moving in a straight line as shown in figure.

The acceleration of the particle.
A. is constant
B. increases linearly with x
C. increases parabolically with x
D. None of these

Answer 1

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