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Question

# Two cars A and B with a mass of 5 kg and 10 kg and initial velocities of 10 msâˆ’1 and 5 msâˆ’1 are racing. Which car exerts more power before coming to rest? (Time taken for both cars to complete the race is 10 seconds):

A

Data insufficient

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B

B

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C

Both exert same power

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D

A

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Solution

## The correct option is D A Let W1 be the work done and P1 be the power exerted by car A. Let W2 be the work done and P2 be the power exerted by car B. Given mass of car A, m1 = 5 kg initial velocity of car Au1=10 ms−1 final velocity of car A, v1=0 (since the car comes to rest) mass of car B, m2 = 10 kg initial velocity of car B u2=5 ms−1 final velocity of car B, v2=0 (since the car comes to rest) Since work done = change in kinetic energy work done by car A = final K.E - initial K.E = mv212−mu212=0−mu212 W1 = 12×m1×u12=0.5×5×100=250, So P1=25010=25 Js−1 work done by car B = final K.E - initial K.E = mv212−mu212=0−mu222 W2​ =12×m2×u22=0.5× 10 × 25 = 125, So P2​ = 12510=12.5 Js−1 Hence A exerts more power than B.

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