Which equation correctly defines impulse?

Which equation correctly defines impulse?

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

Answer: (A)

Impulse is the effect of a force acting over a time interval to change an object's momentum. It is defined as the integral of force over that interval, J = ∫ F dt. When the force is constant, this becomes J = F Δt. The impulse-momentum connection is J = Δp, meaning the impulse equals the change in momentum. So, for a constant force, J = F Δt directly expresses impulse, and in general J = Δp. The other expressions don’t fit: Δp/Δt is the average force, not the impulse; F/Δt has the wrong units for impulse; and Δt is just a time interval, not a momentum change.

Impulse is the effect of a force acting over a time interval to change an object's momentum. It is defined as the integral of force over that interval, J = ∫ F dt. When the force is constant, this becomes J = F Δt. The impulse-momentum connection is J = Δp, meaning the impulse equals the change in momentum. So, for a constant force, J = F Δt directly expresses impulse, and in general J = Δp.

The other expressions don’t fit: Δp/Δt is the average force, not the impulse; F/Δt has the wrong units for impulse; and Δt is just a time interval, not a momentum change.