Conservation of momentum

In all isolated systems, total momentum is conserved:

ptot=ptot.

Example

Car A (2.5 kg) begins at 1.5 m/s [fwd], while Car B (1.5 kg) beings at rest. Car A collides into Car B, and they stick together. What is the velocity of AB after the collision?

We begin with the conservation of momentum,

ptot=ptot,

into which we substitute the individual momenta:

pA+pB=pAB.

Now we can substitute the masses and velocities with

mAvA+mBvB=mABvAB,

and solve for the final velocity:

vAB=mAvA+mBvBmAB.

Substituting the known values where [fwd] is positive, we have

vAB=(2.5 kg)(1.5 m/s)02.5 kg+1.5 kg=0.9375 m/s,

therefore the final velocity is 0.94 m/s [fwd].