Ok. A lap timer is different from a drag race lap timer.
Drag race timers are exactly what they are. Your travel time from start to finish with one lap.
Lap timers are a little more involved because you have more than 1 lap.
The diagram provided in ViSioNXx's post is a little hard to understand because whoever drew it... sucks at drawing schematics lol.
Anyways.... The Infrared beam sensor, Radioshack Part Number 49-551, the project requires is obsolete as of 2009. So you would need to find an alternative.
An alternative to consider is an ultrasonic motion detector. Keep in consideration there is a lag time of 340.29 meters per second with ultrasonic detectors.
So the best way to time vehicles would be infrared detectors. Keep searching on Google until you think you found something suitable for your needs.