You could do it accurately and cheaply using 2 LEDs, 2 Phototransistors, a dual Op-amp configured as 2 comparators and a 3.5mm mini jack and a bit of audio cable to go into your computer's Audio In.
Point an LED at a Phototransistor at the part of the car's run where you want the test to start and put the other one a little way ahead of it. Set the car running and use a sound recorder to sample the clicks made by the comparators as they trigger at the breaking and remaking of each of the LED beams. Look for the start of each event and record the time. Then look for the end of each event and record the times as accurately as you can.
Add the times together (front of car goes past each LED, back of car goes past each LED) and divide by two to get the average.
Measure the distance between the LEDs as accurately as you can.
The linear velocity of the car is the distance traveled divided by the time taken.
Total cost - less than 5 dollars.
Have fun.