I would use photo transistors to start and stop the timer(s). Drill holes in each track at the start and end lines. Place photo transistors in each hole, pull the collector high with a 10K or so resistor. Make a structure that goes above the starting and ending lines which holds LEDs, one per track. The LED would cause the PT's collector to be low when no car is over it and high when the car blocks the LED. The signal from the PT at the starting line starts the timer running, the PT signal at the end stops it.
I would use a smallish uC like a PIC to time them. I'd use a notebook computer and send the results to it for automatic tabulation. You could, of course, use an LCD display driven by the uC to display the results stand-alone.