The drawing shows velocity (v) versus time (t) graphs for two cyclists moving along the same straight segment of a highway from the same point. The second cyclist starts moving at `t = 3 min`. At what time do the two cysclist meet ?

Explanation

Acceleration of cyclist ` A, a_1 = ` slope of straight line `OA = (MC)/4`
Aceeleration of cyclist ` B, a_2 =` slope of straight
` Line ` DB = ((MC))/((4-3)) = (MC)/1 `
:. ` a_1 /a_1 = ((MC))//4)/((MC)//1) = 1/4` …(i)
Let the two cyclist meet after tiem (t), when time is noted from the statrt of cyclist (A). At meeting point, the distatnce coverted by both the cyclist is the same.
So, `1/2 a_1 t^2 = 1/2 a_2(t -3)^2`
or ` a_1/a_2 = ((tt-3)^2)/t_2 = 1/4` [from (i)]`
or ` (t-3)/t = 1/2 or ` 2 t- 6 ` or ` t= 6 min`.