Momentum Formula — p = mv

The momentum formula p = mv explained: quantity of motion, vector nature, conservation idea, and a worked example.

What it means

Momentum measures the quantity of motion — how much oomph a moving object carries. A heavy truck rolling slowly can have the same momentum as a light car speeding, and both are equally hard to stop. Unlike kinetic energy, momentum is a vector: direction matters, which is why two objects can have identical speeds but canceling momenta. The deep power of p = mv is conservation: in an isolated system the total momentum never changes, no matter how violent the collision — a law that survives even into quantum mechanics and relativity.

Variables

Assumptions

• Object treated as a point mass
• Speeds far below the speed of light (non-relativistic)
• p is measured in an inertial reference frame

Derivation

Newton's second law in momentum form is $F = dp/dt$: force is the rate at which momentum changes. For constant mass this reduces to $F = ma$, and integrating a constant force over time gives the impulse–momentum relation $F\Delta t = \Delta p$.

Worked example

Given:

• m = 1500 kg
• v = 20 m/s

1. Write the formula: $p = mv$

2. Substitute: $p = 1500 \times 20$

3. Multiply: $p = 30{,}000\ \mathrm{kg\cdot m/s}$