Question

How can I make calculations and design a toy car running at a speed of 10m/s and which should cover a maximum distance of 30m? The design should consist of springs, gears, shafts, rack, and pinion. Urgent help needed.

Answer 1

the level of information you are asking is depending on the instruments which you have to measure it. So I will try to answer it assuming I am at home, not at Physics laboratory.

So its a simple spring operated car, so when you pull it back, the amount of Potential energy stored is 1/2 kx^2. I hope you know the value of k as it is material dependent, and x is the amount of displacement in spring.Its not linearly equals to displacement on ground but less. Lets assume a tyre of 1 inch diameter when pulled back for 6 inches compresses the spring by 0.5 inch. (Its my self assumed figures). I have ignored thermal energy and sound energy here.

Now when you release it, it will become Kinetic energy and Heat energy due to friction. At any moment if you can measure the speed of the car, then 1/2 mv^2 would give you the Kinetic energy. At that very moment, Difference in PE-KE will give you the energy been lost to surroundings in form of heat and sound. When car finally stops, all energy is lost to surrounding. Simple conservation of energy.

Assumptions - Car is running on flat surface. Car is not electrostatic charged. You are viewing car from same reference where you are standing.Car is a car(matter) not wave.