The given graph shows the variation of velocity (v) with position (x) for a particle moving along a straight line. Which of the following graph shows the variation of acceleration (a) with position (x)?

Question

The given graph shows the variation of velocity (v) with position (x) for a particle moving along a straight line. Which of the following graph shows the variation of acceleration (a) with position (x)? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Given line have positive intercept but negative slope.
So its equation can be written as,

v = - m x + v_{0} \dots (1)

where

m = t an θ = \frac{v _{0}}{x _{0}}

By differentiating with respect to time we get,

\frac{d v}{d t} = - m \frac{d x}{d t} = - m v

Now substituting the value of ‘v’ from equation (1) we get

\frac{d v}{d t} = - m [- m x + v_{0}] = m^{2} x - m v_{0}

a = m^{2} x - m v_{0}

i.e., the graph between a and x should have positive slope but negative intercept on acceleration axis.

Q. The given graph shows the variation of velocity (v) with position (x) for a particle moving along a straight line. Which of the following graph shows the variation of acceleration (a) with position (x)?