Momentum is a vector

Beginner

It has direction, so opposite motions can cancel.

Because momentum has direction, opposite motions subtract. Add momenta component by component in two or three dimensions.

Worked example

A 2 kg cart at +3 m/s and a 3 kg cart at −2 m/s have total p = 0.

Common mistake

Don't add magnitudes.

In more detail

Momentum points in the same direction as velocity. Momentum components add separately along each axis, so you handle each direction in turn.

Analysing a two-car crash at an angle requires separate momentum components along each road direction.
Billiard players compute the direction of the cue ball after a collision using momentum vectors.
Two identical trolleys moving toward each other with equal speeds have zero total momentum, so they can stop dead on impact.

Do momentum components combine like vectors?

Yes. Use the sum of the x components and the sum of the y components separately.

Can momentum be negative?

Yes, it is negative when the velocity points in the chosen negative direction.

Do I need to include direction for momentum?

Yes. Always choose a positive direction and give velocities a sign, otherwise opposite motions will be added instead of cancelled.