Velocity v of a particle moving along x -axis varies with its position (x) as v=α √{x} ; where α

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2.Motion in Straight Line

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The velocity $v$ of a particle moving along $x$-axis varies with its position $(x)$ as $v=\alpha \sqrt{x}$; where $\alpha$ is a constant. Which of the following graph represents the variation of its acceleration (a) with time $(t)$ ?

A

B

C

D

Solution

(c)

$v=\alpha \sqrt{x}$

Squaring both sides $v^2=\alpha^2 x$

Comparing above equation with $3^{\text {rd }}$ equation of kinematics.

$v^2=u^2+2 a x$

$\alpha^2 x =2 a x$

$\Rightarrow a=\frac{\alpha^2}{2}$

$\,\downarrow$

$\text { Constant } \rightarrow \text { not a function of time }$

so,

Standard 11

Physics

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