Which force-time curve has the smaller impulse, A or B?

Question

BlackTom AI · Accepted Answer

Impulse is the area under the force-time curve, i.e., ∫F dt. 
Option A: This option states that curve B has the smaller impulse. To assess this, compare the shaded areas under each curve. The yellow curve A is a very tall, narrow spike with a relatively small base in time, whereas curve B is a broader, lower-height hump with a much larger base in time. The area under B appears larger because the force remains significant over a longer duration, even if its height is lower than the peak of A. Therefore, the impulse associated with the curve A/B pair is not the smaller one asserted here; the area under B is larger than under A.
Option B: This option states that curve A has the smaller impulse. Given the visual comparison, the area under curve A is smaller in width but higher in peak, while curve B sustains a substantial force over a longer interval, yielding a larger area. Since the impulse depends on both height and time duration, the broader, longer curve B accumulates more impulse than the sharp, short curve A. Thus the claim that A has the smaller impulse aligns with the observation that the A-region’s area is smaller than the B-region’s.
Overall, evaluating the two choices in terms of which curve encloses less area under the curve shows that the left/right labeling corresponds to which impulse is smaller, with the longer, wider curve accumulating more impulse than the narrow spike. The key idea is that impulse equals area, and the larger area corresponds to the larger impulse, while the smaller area corresponds to the smaller impulse.

Which force-time curve has the smaller impulse, A or B?Single choice

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