I was in charge of the model, and using skills I've learned across a few projects, quickly made all the materials we had access to into parts, and then started moving the parts around to see how we could lay out our car in a way that made every part fit together.
If you would like to view the model, you can do so here.
As for the actual car, we decided that using a level arm would yield less mechanical advantage than if we used a 2-step pulley reduction. This allowed the back wheels to spin extremely fast with barely any motion, and the mousetrap certainly had more than enough force to deal with the increase in required torque. We had a total pulley ratio of 1:625, which allowed our car to cross quite a large distance. This did put a lot of stress on the car however, so we had to reinforce the fragile components we were given by adding zip ties, hot glue, and making one of the axles slightly wider to reduce the amount of internal stress on the vehicle.
On the right you can see a demo of the car's driving force, with the pulling hand simulating the mousetrap.
Overall, the event was a success and I had a blast making the car with my fellow engineers!