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
$v=Kx$

$\frac{dv}{dt}=K\cdot v$ (from the Eq. (i))
$\frac{dv}{dt}=K\cdot (Kx)=K^{2}x$
$a=K^{2}x$
and $v=-Kx+v_0$
$\frac{dv}{dt}=-K\cdot v=-K\left(-Kx+v_0\right)$
$a=K^{2}x-K{v}_0...(ii)$
So, according to the Eq. (ii).