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Q.

Two cars start in a race with velocities u1 and u2 and travel in a straight line with acceleration ‘α’ and β. If both reach the finish line at the same time, the range of the race is

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a

2(u1-u2)(β-α)2(u1β-u2α)

b

2(u1-u2)β+α(u1α-u2β)

c

2(u1-u2)2(β-α)2

d

answer is A.

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Detailed Solution

s=u1t+12αt2 (for first car) s=u2t + 12βt2(for second car) 0=( u1-u2)t +12(α-β)t2 t=2(u2-u1)(β-α) s =2(u2-u1)u1β-α+12α[(u2-u1)(β-α)]2 Simplifying, s= 2(u1-u2)(u1β-u2α)(β-α)2
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Two cars start in a race with velocities u1 and u2 and travel in a straight line with acceleration ‘α’ and β. If both reach the finish line at the same time, the range of the race is