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  4. Velocity versus displacement curve of a particle moving in straight line is shown in the figure. From a point P, a line is drawn perpendicular to displacement axis and line P R is drawn normal to the curve at P. Find the instantaneous acceleration of the particle at point P.

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Q. Velocity versus displacement curve of a particle moving in straight line is shown in the figure. From a point $P$, a line is drawn perpendicular to displacement axis and line $P R$ is drawn normal to the curve at $P$. Find the instantaneous acceleration of the particle at point $P$.Physics Question Image

Motion in a Plane

Solution:

Slope of line $Q R=\tan \alpha=-\frac{P Q}{Q R}$
image
$\Rightarrow \tan \alpha=\frac{-v}{1}$
Slope of line $A B$ at $P=\frac{d v}{d s}[a t P]=-\frac{1}{\tan \alpha}$
$\Rightarrow \frac{d v}{d s}=\frac{1}{v} a_{p}=\frac{v d v}{d s}$
$=\frac{v \times 1}{v}=1 \,m / s ^{2}$