Which statement best expresses Newton's second law in impulse form?

Which statement best expresses Newton's second law in impulse form?

• A. J = F Δt
• B. J = Δt
• C. J = Δp
• D. J = Δp / Δt

Answer: (C)

Impulse is the total effect of a net force over a time interval, and it directly changes an object's momentum. The precise relation is that the impulse equals the change in momentum: J = Δp. This comes from the fact that impulse is defined as the integral of force over time, J = ∫ F dt, which, by Newton’s second law, equals p_final − p_initial. This holds no matter how the force varies during the interval. If the force is constant, you could write J = FΔt, but that’s only a special case. The option J = Δp/Δt would give average force, not the total impulse, and J = Δt isn’t dimensionally meaningful for impulse. So the statement J = Δp best expresses the impulse form of Newton’s second law.

Impulse is the total effect of a net force over a time interval, and it directly changes an object's momentum. The precise relation is that the impulse equals the change in momentum: J = Δp. This comes from the fact that impulse is defined as the integral of force over time, J = ∫ F dt, which, by Newton’s second law, equals p_final − p_initial. This holds no matter how the force varies during the interval.

If the force is constant, you could write J = FΔt, but that’s only a special case. The option J = Δp/Δt would give average force, not the total impulse, and J = Δt isn’t dimensionally meaningful for impulse. So the statement J = Δp best expresses the impulse form of Newton’s second law.