Initially car `A` is `10.5 m` ahead of car `B`. Both start moving at time `t = 0` in the same direction along a straight line. The velocity-time graph of two cars is shown in figure. The time when the car `B` will catch the car `A`, will be.

Options

A. `t = 21 sec`
B. `t = 2 sqrt(5) sec`
C. 20 sec
D. none

Answer

A

Explanation

Let they meet at `C`.
For car `A : x = v_A t rArr x = 10 t`
Acceleration of car `B : a_B = tan 45^@ = 1 m//s^2`
for car `B : x + 10.5 = (1)/(2) a_B t^2`
`rArr 10t + 10.5 = (1)/(2) 1 t^2`
`rArr t^2 - 20 t - 21 = 0`
`rArr (t - 21)(t + 1) = 0`
`rArr t = 21 s`.