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  4. 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)?

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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)?Physics Question Image

KCETKCET 2019Motion in a Straight Line

Solution:

Given line have positive intercept but negative slope.
So its equation can be written as, $v=-m x+v_{0} \quad\ldots\left(1\right)$
where $m=tan\, \theta=\frac{v_{0}}{x_{0}}$
By differentiating with respect to time we get, $\frac{d v}{d t}=-m \frac{d x}{d t}=-mv$
Now substituting the value of ‘v’ from equation (1) we get
$\frac{d v}{d t}=-m\left[-mx+v_{0}\right]=m^{2}x-mv_{0}$
$a=m^{2}x-mv_{0}$
i.e., the graph between a and x should have positive slope but negative intercept on acceleration axis.