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

`(3)/(4)` ; Nowhere on the route, overtaking is possoble.

Explanation

`t_(1)+t_(2)=2 rArr (S)/(30)+(S)/(60)=2 rArr S=40 km`

Tolat distance`=80 km`
`80=(1)/(2) a (2)^(2)`,
`a=40 km h^(-2)`,
`t_(1)=(40)/(30)=(4)/(3) h, t_(2)=(40)/(60)=(2)/(3)h`
For `t l t(4)/(3) h`: If their speeds are equal
`30=at rArr t=(3)/(4) h`, so speeds become equal at `t=(3)/(4) h l t (4)/(3)h`
So not possible.
For `t l t (4)/(3) h`: If theri speeds are equal,
`60=at rArr t=(3)/(2) h`
So their speeds other: `40+60 (t-(4)/(3))=((4)/(3)) =(1)/(2) at^(2)`
`rArr 40+60t-80=20t^(2) rArr t^(2)-3t+2=0`
`rArr(t-1)(t-2)=0 rArr t=1 h` (not valid), `2 h`
So nowhere on the route, overtaking is possible.