Two motor cars start from A simultaneously & reach B after 2 hour. The first car travelled half the distance at a speed of `v_(1)=30 km hr^(-1)` & the other half at a speed of `v_(2)=60 km hr^(-1)`. The second car covered the entire with a constant acceleration. At what instant of time, were the speeds of both the vehicles same? Will one of them overtake the other enroute?

Answer

0.75 hr, 1.5 hr after the moment of departure, No overtaking

Explanation

For A : `30t_(1)=S//2=60 (2-t_(1))rArr t_(1)=4//3` hr (Here S is the total distance and `t_(1)` is time up to which A's speed is `30 km//hr`)
For B : `1/2xxaxx2^(2)=(30xx4/3)xx2=S`
`rArr a=40 km//hr^(2)`
(i) (a) `v_(B)=40t=30rArrt=0.75` hr
(b) `v_(B)=40t=60rArr t=1.5` hr
(ii) there is no overtaking.