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Momentum & Impulse Calculator

Apply the impulse-momentum theorem (J = FΔt = Δp) to find an object's final momentum and velocity after a force acts on it for a given time.

Initial momentum
6 kg·m/s
Impulse (J = FΔt)
10 kg·m/s
Final momentum
16 kg·m/s
Final velocity
8 m/s
Change in velocity (Δv)
5 m/s

How it works

An object's momentum is p = m × v (mass times velocity). The impulse-momentum theorem says a net force F applied for a duration t changes momentum by exactly J = F × t — this quantity is called impulse. So the final momentum is simply the initial momentum plus the impulse, p_final = p_initial + J, and the final velocity follows as p_final ÷ m.

Impulse and momentum share the same physical units (mass × velocity), even though impulse is computed from force × time — a newton-second and a kilogram-meter-per-second are the exact same SI unit, since a newton is itself kg·m/s². This calculator's imperial mode carries that through consistently: momentum, impulse, and final momentum are all shown in the same lb·mph units, so 'final momentum = initial momentum + impulse' still checks out by simple addition of the displayed numbers.

A negative force represents one that opposes the direction of motion (like braking or drag) rather than one that speeds the object up — enter time as the duration that opposing or driving force acts for.

FAQ

What's the difference between momentum and impulse?

Momentum (p = mv) describes an object's current motion at an instant. Impulse (J = FΔt) describes the total effect of a force acting over a stretch of time — it's the *change* in momentum a force produces, not a property of the object by itself. A large force applied briefly and a small force applied for a long time can deliver the exact same impulse.

Why can force and velocity be negative here?

Momentum and force are vector quantities — along a single line of motion, sign indicates direction. A negative initial velocity or a negative (opposing) force is physically normal, e.g. a car braking has a force opposite its direction of travel. Mass and time, on the other hand, are always positive.

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