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Question

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 1m/s2 and car Y moves with uniform acceleration of 1.1m/s2. If both the cars reach the winning post together find the length of the track.

A
1000 m
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B
2000 m
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C
2500 m
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D
2280 m
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Solution

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+at2/2=8t+0.5t2........ (1)

The equation of motion for the car Y will be S=ut+at2/2=5t+0.55t2........ (2)
equating both equations we get .(0.550.5)t2+(58)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

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