A moving object's dynamical state can be described by its linear momentum:

$$\mathbf p=m\mathbf v.$$

Momentum is a vector. Its direction is the direction of velocity, and its magnitude increases with both mass and speed.

Momentum of a system

For several particles, total momentum is the vector sum

$$\mathbf P=\sum_i\mathbf p_i.$$

Two equal masses moving with equal speeds in opposite directions can therefore have zero total momentum even though both are moving.

Momentum versus kinetic energy

Momentum and kinetic energy both depend on motion but behave differently:

$$p=mv,$$

$$K=\frac12mv^2.$$

Momentum is a vector and can cancel between different directions. Kinetic energy is a nonnegative scalar and adds regardless of direction.

Why momentum matters

Newton's second law can be expressed more generally as a relationship between net force and the rate of change of momentum. This makes momentum especially useful for interactions that occur over short times, where forces may be large and rapidly varying.