Question

wo bumper cars move toward each other. The cars hit and bounce off of each other. The momentum before the collision will be equal to the
after.

Answer 1

Yes — the total momentum of the two-car system is the same before and after the collision, provided there is no significant external impulse during the collision (i.e., the pair is effectively an isolated system in the direction you’re considering).

In equation form (vector quantities):
m1 v1 + m2 v2 = m1 v1' + m2 v2'

Why this holds:
- During the collision the cars exert equal and opposite forces on each other (Newton’s third law). Those internal forces change the individual momenta but cancel in the sum, so the total momentum is unchanged.
- If external forces (friction with the ground, pushes from the arena) produce a significant net impulse during the short collision time, total momentum need not be conserved.

Notes:
- Momentum is a vector: directions matter (opposite directions have opposite signs).
- Kinetic energy need not be conserved — collisions can be elastic (KE conserved) or inelastic (some KE lost to deformation, heat, etc.), but total momentum is conserved in both as long as external impulses are negligible.
- The center-of-mass velocity of the two-car system remains constant through the collision.