The impulse-momentum theorem states what relation between impulse and momentum?

The impulse-momentum theorem states what relation between impulse and momentum?

• A. F = ma
• B. J = Δp
• C. p = mv
• D. W = F d

Answer: (B)

The impulse-momentum connection says that the total impulse imparted to an object equals the change in its momentum. In symbols, impulse J is the integral of force over time, J = ∫ F dt, and this equals Δp = p_f − p_i. So impulse directly measures how much the object's momentum changes due to the force acting on it. This means if mass stays the same, Δp = mΔv, so the impulse also equals m(v_f − v_i). If the force is constant, you can write J = FΔt, but the fundamental statement is J = Δp, which holds in general. Why the other ideas don’t capture this relationship: F = ma links instantaneous force to acceleration at a moment in time, not the cumulative effect over a time interval. p = mv is the momentum itself, not the change in momentum. W = Fd concerns work and energy, not momentum.

The impulse-momentum connection says that the total impulse imparted to an object equals the change in its momentum. In symbols, impulse J is the integral of force over time, J = ∫ F dt, and this equals Δp = p_f − p_i. So impulse directly measures how much the object's momentum changes due to the force acting on it.

This means if mass stays the same, Δp = mΔv, so the impulse also equals m(v_f − v_i). If the force is constant, you can write J = FΔt, but the fundamental statement is J = Δp, which holds in general.

Why the other ideas don’t capture this relationship: F = ma links instantaneous force to acceleration at a moment in time, not the cumulative effect over a time interval. p = mv is the momentum itself, not the change in momentum. W = Fd concerns work and energy, not momentum.