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)

(c)

(d)

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Answer:

Correct Answer: 6. (a)

Solution:

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

$$ \begin{aligned} & v=-\frac{v _0}{x _0} x+v _0 \cdots(i)\\ & a=\frac{d v}{d t}=-\frac{v _0}{x _0} \frac{d x}{d t}=-\frac{v _0}{x _0} v \end{aligned} $$

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

$$ a=-\frac{v _0}{x _0} \quad-\frac{v _0}{x _0} \quad x+v _0 \Rightarrow a=\frac{v _0}{x _0} \quad x-\frac{v _0^{2}}{x _0} $$

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



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