First slide

Graphical representation-Motion in 1 d

Question

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

Difficult

A

16/3 sec
B

10 sec
C

8 sec
D

12 sec

Solution

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

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