Which equation correctly relates impulse to momentum?

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

Answer: (D)

Impulse is what changes an object's momentum. The impulse delivered to an object equals the change in its momentum, so J = Δp. If the force acting on the object is constant over the time interval, that same impulse can be written as J = F Δt. Since both expressions describe the same impulse, they are equal, giving J = Δp = F Δt.

The first part, J = Δp, is the fundamental link between impulse and momentum. The second part, F Δt, is the practical way to compute impulse when the force stays constant. If the force isn’t constant, the impulse is the integral of force over time, not simply F Δt, but for many problems the assumption of constant force makes J = Δp = F Δt a complete and useful statement.