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 :

Options

A. `40` sec.
B. `80` sec.
C. `60` sec.
D. `100` sec.

Answer

C

Explanation

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`