There are a few commercial RC Lap timing solutions that use IR. The two challenges for IR are
1) Sunlight - the sensor needs to be in a shade of some sort to prevent saturation by sunlight
2) Line of sight - there needs to be a clear path for the light between the transponder and the sensor
The solution is to point the sensors down at the ground (away from the sun), a string of downward facing sensors are placed on a sensor bridge across the track, pointing the sensors down and having lots of the overcomes both 1) and 2).
All you need to Arduino to do is act as a concentrator for reading the sensors and sending car ids and signals to a PC over serial.
Your challenges will be -
1) Defining a protocol to identify each car in the time you have available i.e. if your cars are passing at 20 meters per second, you only have a twentieth or less of a second to read the car id.
2) The Arduino takes a few millionths of a second to process an interrupt, as your signal is likely to be several bits (interrupts) long, there is a lot of work for the Arduino to do to in a short time, especially if there are 10 cars sending their ids at the the same time, you need to take the time it takes the Arduino to process multiple interrupts into the protocol design.
As IR parts are so cheap, you can easily work this out on the bench for a few dollars in parts. My design is for a self contained timing system for one car so I have not needed to address a multi car protocol but the commercial system our club uses manages upto eight cars using IR.
A final thought - if its off road racing where dust and mud will block the emitters and detectors, IR isn't going to work well.