The given graph shows the variation of velocity with displacement. Which, one of the graphs given below correctly represents the variation of acceleration with displacement

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TestHub · Accepted Answer

The v - x equation from the given graph can be written as

$v = (- \frac{v_{0}}{x_{0}}) x + v_{0}$ ... (i)

$a = \frac{d v}{d t} = (- \frac{v_{0}}{x_{0}}) \frac{d x}{d t}$

$= (- \frac{v_{0}}{x_{0}}) v$

Substituting v from Eq. (i) we get,

$a = (- \frac{v_{0}}{x_{0}}) [(- \frac{v_{0}}{x_{0}}) x + v_{0}]$

$a = {(\frac{v_{0}}{x_{0}})}^{2} x - \frac{v_{0}^{2}}{x_{0}}$

Thus, a-x graph is a straight line with positive slope and negative intercept.
Correct answer is

Physics - Kinematics Question with Solution | TestHub

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