In a perfectly elastic collision where the objects colliding are of equivalent mass, then yes, the sum of the speeds of the objects before the collision would equal the sum of the speeds of the objects after the collision. However, the real world isn't an ideal scenario. Some of the energy in a collision is given off as sound, some is given off as heat, some energy is used to deform or break the objects colliding. The energy of the system is conserved, but not the speed or even the momentum.

 

The momentum will be conserved if there are no net external forces (which is usually assumed when analyzing collisions).

 

If one wants an easy example to demonstrate that speed is not conserved, consider a completely inelastic collision. With the target at rest, the final speed is always less than the incoming particle's speed.

If one wants an easy example to demonstrate that speed is not conserved, consider a completely inelastic collision. With the target at rest, the final speed is always less than the incoming particle's speed.

 

If you want a practical demonstration, get three balls of descending size (lets say one of those small, bouncy footballs, a tennis ball and a table tennis ball), put one on top of the other so that you have this:

 

 

Now drop them from a height of, say, 50cm.

 

When they hit the ground and bounce back up again, the smallest ball will fly off about 20m into the air or more

 

(Who says you don't learn things from the pseudoscience forum)