SATHEE: Kinematics 4 Question 6

Kinematics 4 Question 6

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

$(2005, 2 M)$

(a)

(b)

(d)

Show Answer

Solution:

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

$\begin{aligned} v = - \frac{v_{0}}{x_{0}} x + v_{0} \\ a = \frac{d v}{d t} = - \frac{v_{0}}{x_{0}} \frac{d x}{d t} = - \frac{v_{0}}{x_{0}} v \end{aligned}$

Substituting $v$ from Eq. (i) we get,

$a = - \frac{v_{0}}{x_{0}} - \frac{v_{0}}{x_{0}} x + v_{0} \Rightarrow a = \frac{v_{0}}{x_{0}} x - \frac{v_{0}^{2}}{x_{0}}$

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

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Kinematics 4 Question 6

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

Solution:

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