Some thoughts on the design of mice are given below. Much more information is available from other sources so some hunting around will pay dividends.
This is a test of acceleration and straight-line steering ability. It is unlikely that an un-steered mouse will be able to get to the end accurately enough to avoid hitting the side walls on the way. For the start, mice can have their motors running and then be dropped on the track when the lights turn green or can be started by any other means e.g. by the use of a simple microswitch which activates the power when the mouse is lowered, by a toggle switch flicked by the handler or by some more sophisticated means. Tyres having good grip will be essential (especially for braking) and 4-wheel drive might help. A number of power sources could be considered, electric, rubber, clockwork or flywheel are possible options. Mice could be adapted from Radio-controlled car kits - but cannot be controlled by radio. The mouse may be travelling quite fast at the end of the run so it will need to be strong enough to withstand running into the end if the brakes fail. The end of the track centre line tape can be used to activate brakes as could detection of the timing beam. Alternatively the finish line gantry may be used to trip a braking circuit by means of a microswitch having an extended vertical arm which is actuated by hitting (lightly!) the horizontal part of the gantry. For practice at School a test track could be made out of half of a single standard sheet of MDF (0.6m wide by 2.4m long) with 5cm x 2cm walls made from softwood. An end of track arresting system could be made from a table tennis net held in place by elastic bands. This simple track would be sufficient to check the start method, acceleration, steering and activation of the brakes within a short distance.
To compete at this level requires a mouse that can steer or turn both left and right whilst accurately following the edge of the track. Absolute speed is less important than keeping on track and getting a complete lap in to record a time. Analogue and computer controlled mice should be able to compete equally if carefully designed but a mouse which learns the circuit on the first few laps is likely to be amongst the winners as it can be programmed to go faster along the straights and will know which way to turn for the next corner.
To compete at this level requires a mouse that only needs to steer one way. As a consequence the mechanics, electronics and sensors can be quite simply made. Mice can be made from constructional sets such as Lego or Meccano, be based around a kit such as that produced by Swallow Systems or be made from scratch using any available components. Accurately following of the track edge is important but speed is even more important. Analogue and computer controlled mice should be able to compete equally if carefully designed. A compact Low Mass mouse is likely to do well in this event.
Remember To finish first, first you must finish.