two cars start moving from rest with uniform acceleration `a=4 m//s^(2)` and ` 8 m//s^(2)` towards each other from points A and B. the distance between points is 96 m

Options

A. Their relative velocity V at the time of the meeting is 24 m/s
B. The first car covers one third of the total distance till then
C. The two cars are again at a distance 96 m 8 seconds after meeting.
D. The first car has a speed of 16 m/s at the time meeting.

Answer

BD

Explanation

`v_(rel)^(2) =u_(rel)^(2)xx2a_(rel)s_(rel)`
`=2xx12xx96`
`v_(rel) =sqrt(24xx24xx4) rArr 48m//s`

`S_(1)=1/2xx4xxt^(2)`
`S_(2)=1/2xx8xxt^(2)`
`(S_(1))/(S_(2)) =1/2`
`S_(rel)=1/2 a_(rel)t^(2)`
`96=1/2xx12xxt^(2), " " t=4 sec`
`S_(rel)=1/2xx12xx8^(2) =6xx64 =384`
`V_(1)=a_(1)t =16 m//s`