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  4. Graph of (1 / v) vs. x for a particle under motion is as shown, where v is velocity and x is position. The time taken by particle to move from x=4 m to x=12 m is

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Q. Graph of $(1 / v)$ vs. $x$ for a particle under motion is as shown, where $v$ is velocity and $x$ is position. The time taken by particle to move from $x=4\, m$ to $x=12\, m$ isPhysics Question Image

Motion in a Straight Line

Solution:

First find relation between $v$ and $x$
$\frac{1}{v}=\frac{3 x}{16}-\frac{1}{4}$
$\Rightarrow \frac{d t}{d x}=\frac{3 x}{16}-\frac{1}{4}$
$\Rightarrow \int\limits_{t_{1}}^{t_{2}} d t=\int\limits_{4}^{12}\left(\frac{3 x}{16}-\frac{1}{4}\right) d x$
Solve to get $t_{2}-t_{1}=10\, s$