In a perfectly elastic collision, both momentum and kinetic energy are conserved. The collision between the carts involves no external forces along the track, so the total momentum (the combined mass times velocity) before and after the collision stays the same. At the same time, no energy is lost to deformation, heat, or sound in an ideal elastic collision, so the total kinetic energy before equals the total kinetic energy after. That combination—momentum conservation from the internal impulses and kinetic energy conservation from the absence of energy loss—defines the ideal elastic case. The other descriptions miss one of these essential features: momentum alone ignores the energy bookkeeping, or kinetic energy alone ignores that momentum must also be preserved in the absence of external forces.

Speed is the rate at which distance is covered. When you divide the distance travelled by the time it takes, you obtain speed. This doesn't include direction—that would be velocity. For example, traveling 100 meters in 20 seconds gives a speed of 5 meters per second. Distance describes how far you went, time describes how long it took, and acceleration describes how quickly your velocity is changing.

Momentum depends on mass and velocity because it is the product p = m v. If you increase the mass while keeping velocity the same, momentum goes up; if you increase velocity with the same mass, momentum also goes up. Time, acceleration, position, or force don’t set the current momentum directly (time and acceleration describe how momentum changes, and force relates to that change via F = dp/dt). In short, the current momentum is determined by how much matter there is (mass) and how fast it’s moving (velocity).

Staying at rest happens when the total force on the object is zero. For a stationary object on a surface, gravity pulls downward while the surface pushes upward with a normal force. These two forces balance each other, so the net force is zero and there is no acceleration. That’s why two forces are acting in this common scenario. If other interactions were present (like a push or friction), there could be more forces, but in the simple case of a stationary object on a surface, two forces balance to keep it at rest.