Two ball bearings of mass m each moving in opposite directions with equal speed v collide head on with each other. Predict the outcome of the collision, assuming it to be perfectly elastic. 

Here, m₁ = m₂ = m,   u₁ = v,   u₂ = −v

Velocity of the two balls after perfectly elastic collision between them are:

v₁ = [(m₁ − m₂)u₁ + 2m₂u₂] / (m₁ + m₂)

= [0 + 2m(−v)] / (m + m) = −v

v₂ = [(m₂ − m₁)u₂ + 2m₁u₁] / (m₁ + m₂)

= [0 + 2mv] / (2m) = v

After collision, the two ball bearings will move with the same speeds, but their directions of motion will be reversed.