Question

Velocity $ (v) $ versus displacement $ (x) $ plot of a body moving along a straight line is as shown in the graph. The corresponding plot of acceleration $ (a) $ as a function of displacement $ (x) $ is

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

The given graph
$v=K x$

$\frac{d v}{d t}=K \cdot v\,\,\,$ (from the Eq. (i))
$ \frac{d v}{d t} =K \cdot(K x)=K^{2} x $
$ a=K^{2} x$
and $v=-K x+v_{0}$
$ \frac{d v}{d t} =-K \cdot v=-K\left(-K x+v_{0}\right) $
$ a =K^{2} x-K v_{0} \,\,\,...(ii)$
So, according to the Eq. (ii).