Two motor cars start from `A` simultaneouslu and reach `B` after `2 h`. The first car travelled half thedistance at a speed of `30 km h^(-1)` and theother half at a speed of `60 km d^(-1)` The second car started from rest and covered the enetire distance with a constant acceleration. At what instant of time were the speeds of both the vehicles same? Will one of them overtake the other?

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.