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Q.

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

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a

$16 / 3 s$

b

$8 s$

c

$10 s$

d

$12 s$

answer is B.

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Detailed Solution

We know that

$V = \frac{d x}{d t} \Rightarrow d t = \frac{1}{V} d x$

$\int_{t_{1}}^{t_{2}} d t = \int_{4}^{12} \frac{1}{V} d x = A r e a$

$t_{2} - t_{1} = (8 \times \frac{1}{2}) + \frac{1}{2} \times 8 \times \frac{3}{2} = 10 s$

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