Impulse J = FΔt = Δp
Overview
Impulse is the product of force and the time for which it acts: J = FΔt. The impulse-momentum theorem states that impulse equals change in momentum: FΔt = Δp = mv − mu. The area under a F–t graph equals the impulse. A large force over a short time (like a bat hitting a ball) delivers the same impulse as a small force over a longer time.
Impulse — J = FΔt = Δp
Impulse (J) is defined as the product of the net force and the time interval over which it acts: J = F · Δt. By Newton's 2nd Law: J = Δp (impulse equals change in momentum). Impulse is a vector. Unit: N·s = kg·m/s. On a F–t graph, the area under the curve equals the impulse (and thus the change in momentum). This is important when force varies with time — integrate (or find the area).
Why airbags and foam reduce injury
Impulse = change in momentum = Δp is fixed (e.g., going from 60 km/h to 0). The total impulse doesn't change. But impulse = F × Δt. If you increase Δt (softer stop — longer time), then F is smaller. Airbags, foam padding, and crumple zones all extend the stopping time Δt, reducing the peak force and injury. A gymnast bending their knees on landing does the same.
- ⚠Forgetting that momentum change takes direction into account — v_f and v_i are vectors
- ⚠Using Δp = m × Δ|v| instead of Δp = m(v_f − v_i) — you must consider signs/direction