Impulse

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A football of mass 0.4 kg is kicked from rest and leaves the foot with a speed of 25 m/s after the foot is in contact with it for 0.05 s. What is the impulse delivered to the football during the kick?

RankGuru · Accepted Answer

Drawing from NCERT Class 11, Chapter 5 (Laws of Motion), impulse is defined as the product of the average force and the time for which it acts, and by the impulse-momentum theorem it equals the change in linear momentum of the body. Since the football starts from rest, its initial momentum is zero, and its final momentum is m v = 0.4 × 25 = 10 kg·m/s. Therefore the impulse delivered is 10 N·s, which numerically equals the change in momentum. Note that the contact time would be needed only if the question asked for average force (which would be 10 / 0.05 = 200 N). Option 5 N·s halves the momentum without reason. Option 200 N·s is actually the average force in newtons, not the impulse, and confuses the two quantities. Option 2.5 N·s divides incorrectly by the speed. Plausibility check: impulse and momentum share the same units, since 1 N·s equals 1 kg·m/s, so 10 N·s is dimensionally consistent and matches the momentum gained, confirming the answer.

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