A railroad car of mass m is moving at speed v when it collides with a second railroad car of mass m which is at rest. the two cars lock together instantaneously and move along the track. what is the speed of the cars immediately after the collision?

v/2 This is an exercise in the conservation of momentum. The collision specified is a non-elastic collision since the railroad cars didn't bounce away from each other. For the equations, I'll use the following variables. r1 = momentum of railroad car 1 r2 = momentum of railroad car 2 x = velocity after collision Prior to the collision, the momentum of the system was r1 + r2 mv + m*0 So the total momentum is mv After the collision, both cars move at the same velocity since it was non-elastic, so r1 + r2 mx + mx x (m + m) x (2m) And since the momentum has to match, we can set the equations equal to each other, so: x (2m) = mv x (2) = v x = v/2 Therefore the speed immediately after collision was v/2