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Graph of position (x) vs inverse of velo...

Graph of position `(x)` vs inverse of velocity `((1)/(v))` for a particle moving on a straight line is as shown. The time taken by the particle to move from `x = 3m` to `x = 15` is :

A

`40` sec.

B

`80` sec.

C

`60` sec.

D

`100` sec.

Text Solution

Verified by Experts

The correct Answer is:
C
the equation of the straight line shown in the graph is
`x = (2)/(v) = - 1`
But `v = (dx)/(dt)`
`:. x = (2dt)/(dx) -1 `
`rArr xdx = 2 dt - dx`
`rArr overset(15)underset(3)intxdx = 2 overset(1)underset(0)intdt - overset(15)underset(3)intdx`
`rArr (1)/(2)[225 - 9] = 2t - [15 - 3]`
`rArr 108 + 12 = 2t , t = 60 s`
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