1. Tardigrade
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  4. The velocity v of a particle moving along x-axis varies with its position (x) as v=α √x ; where α is a constant. Which of the following graph represents the variation of its acceleration (a) with time (t) ?

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Q. 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 $(t)$ ?

Motion in a Straight Line

Solution:

$v=\alpha \sqrt{x}$
Squaring both sides $v^{2}=\alpha^{2} x$
Comparing above equation with $3^{\text {rd }}$ equation of kinematics.
$v^{2}=u^{2}+2 a x$
$\alpha^{2} x=2 a x$
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