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)
Show Answer
Answer:
Correct Answer: 6. (a)
Solution:
- 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.
