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Mouse trap powered vehicle competitions are usually associated with Science or Technology  challenges at school.
The Design and Technology  may be, 'To design, build, test and run a mouse trap powered vehicle, where the mouse trap's spring is the only means of propulsion.'

Considerations in the design and in the making may centre around,
1. Friction
 2. Elastic Potential Energy/Tension
3. Levers/Machines

In most cases the design brief will allow the mouse trap to be fitted with an extension arm which will allow increased performance to occur.
Consider allowing students to work in pairs or groups.
Once constructed a fair test might be devised where the greatest distance travelled might be measured.
Distance travelled:
A basic design  should propel the vehicle about 1 to 2 metres. However a more sophisticated design may propel the vehicle over 30 metres.
The essential building instructions.
A string is attached to the mouse trap's lever arm and then attached to the drive axle. The string has a loop tied at the axle end; this loop is caught by a hook on the axle (a cable tie cut very short will work well) so that the string is attached to the axle BUT it is allowed to release itself after the pulling force is completed. It is important to have the hook on the axle so that the string will simple slip off.
 
Wind the wheels in the direction opposite to the motion you want the mouse trap car to travel.  Do not push on the mousetrap's lever arm during this process, you want the string to be tightly wound around the axle.

Once the car is released, the string is pulled off the axle and it causes the wheels to rotate propelling the vehicle. If the mousetrap is located too close to the drive axle, the wheels may spin at the start, wasting energy. If the mouse trap is located too far from the drive axle there will not be insufficient  force to propel the racer. Try the mouse trap in several locations in order to get the vehicles best performance.