Two cars X and Y start off to a race on a straight path with initial velocities of 8 m/s and 5 m/s respectively. Car X moves with uniform acceleration of $1{m/s}^2$ and car Y moves with uniform acceleration of $1.1{m/s}^2$. If both the cars reach the winning post together find the length of the track.

The correct option is D 2280 m
Suppose the winning track is of $S$ $meter$ then $time$ taken by both cars should be $same.$

The equation of motion for the car $X$ will be $S=ut+a{t}^2/2=8t+0.5t^2$........ (1)

The equation of motion for the car $Y$ will be $S=ut+a{t}^2/2=5t+0.55t^2$........ (2)

equating both equations we get $.(0.55-0.5)t^2+(5-8)t=0$ or $t=60second$

so the distance $S$ can be calculated by putting $t=60$ in any equation,

putting it in equation-1

we get $S=480+1800=2280meter$