The impulse applied to an object equals the change in its momentum. If a force acts on an object for time Δt, the impulse is J = F Δt. Which statement is correct?

The impulse applied to an object equals the change in its momentum. If a force acts on an object for time Δt, the impulse is J = F Δt. Which statement is correct?

• A. The impulse is equal to the area under the force-time curve
• B. The impulse is equal to the change in velocity
• C. The impulse is equal to the work done
• D. The impulse is independent of time

Answer: (A)

Impulse is the cumulative effect of a force acting over a time interval, and it equals the change in momentum. Because impulse is defined as J = ∫ F dt, it is exactly the area under the force–time graph. If the force is constant, this area simplifies to F Δt, but the core idea is the integral, which geometrically represents that area. This also connects to the impulse–momentum relationship: impulse equals the change in momentum, Δp = m Δv, so impulse equals mass times the change in velocity. It’s not simply the change in velocity unless you know the mass. Impulse isn’t the work done, since work is ∫ F ds (area under the force–displacement curve), not under the force–time curve. And impulse does depend on time because changing how long the force acts changes the area under the curve. So the correct idea is that impulse equals the area under the force–time curve.

Impulse is the cumulative effect of a force acting over a time interval, and it equals the change in momentum. Because impulse is defined as J = ∫ F dt, it is exactly the area under the force–time graph. If the force is constant, this area simplifies to F Δt, but the core idea is the integral, which geometrically represents that area. This also connects to the impulse–momentum relationship: impulse equals the change in momentum, Δp = m Δv, so impulse equals mass times the change in velocity. It’s not simply the change in velocity unless you know the mass. Impulse isn’t the work done, since work is ∫ F ds (area under the force–displacement curve), not under the force–time curve. And impulse does depend on time because changing how long the force acts changes the area under the curve. So the correct idea is that impulse equals the area under the force–time curve.