Impulse-Momentum Calculator
Enter force, time, mass and initial velocity to compute impulse and final velocity via J = Δp = F·Δt = m·Δv.
Input Data
Results
At a glance:The impulse-momentum theorem states that the impulse delivered by a net force over a time interval equals the change in momentum: J = ∫F dt = F_avg·Δt = Δp = m·(v_f − v_i). Impulse (N·s) and momentum (kg·m/s) share the same units. It is the integral form of Newton's second law (F = dp/dt). A large force over a short time (hard impact) or a smaller force over a longer time (airbag, crumple zone) can give the same impulse — extending Δt reduces peak force, the principle behind safety design. This tool computes J and v_f from F, Δt, m and v_i.
Formula
Impulse: J = F·Δt
Momentum change: Δp = m·(v_f − v_i)
J = Δp
$$J = F t = \Delta p = m \Delta v$$How to Use
- Enter the average force F (N) and time Δt (s).
- Enter the mass m (kg) and initial velocity v_i (m/s).
- The calculator returns the impulse J and final velocity v_f.
Case Studies
Catching a ball
m = 0.15 kg, v_i = 20 m/s, F_avg = 30 N.
J = m·Δv; to stop, Δp = 3 kg·m/s, Δt = 3/30 = 0.1 s.
Pulling hands back increases Δt, lowering F.
FAQ
How does this relate to safety?
For a fixed change in momentum, increasing the collision time Δt lowers the average force F = Δp/Δt — airbags and crumple zones extend Δt to reduce injury.
Is impulse a vector?
Yes, in the direction of the net force; it equals the vector change in momentum.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.