**Adding velocities**

Consider two objects. The first object moves
with velocity * v *relative to the second object, while the second
object moves with velocity

However, this formula would allow the observed velocity to exceed the speed of light, so it cannot be right. When relativistic effects are included, the correct expression is instead found to be

where we assume **u** and **v**
are along the same direction.
One can check that this resultant velocity never exceeds the speed of light, by working it out
for the extreme case that * u* (or

Velocity addition problems can be stated in
many ways, often with subtraction of velocities being required rather than addition. A good
strategy for approaching these problems is to always write the Newtonian expression first.
Then use the relativistic expression above, assigning * u* and