Question

# Two cars A and B are moving in same direction. Car A is moving with speed 10 m/s and at a distance 80 m behind car B which starts from rest and with uniform acceleration ao. The maximum value of ao for which car A can reach car B

A
18m/s2
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B
78m/s2
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C
516m/s2
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D
38m/s2
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Solution

## The correct option is C 516m/s2Suppose after time t the car A reaches the the car B then distance traveled by B i.e. xB and the distance by A i.e. xA should be such that xA=xB+gap because A was behind B or xA=xB+80m ...(1)Now as A moves with constant velocity so xA=10×tand B is moving with acceleration and initially at rest (u=0) so xB=0+a0t2=a0t2putting above values in equation-1 we get 10t=a0t2+80 If car A catches car B then we should get some value of t i.e. the root of above eqaution should be REAL.So the discriminant should be positive i.e 102−4×a0×80≥0 or a0≤516m/s2

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