I'm in engineering school and we have a project: we have to build a amphibioues vehicle; I'm looking for a formula.
Our vehicle has to go as far as possible with its unique source of energy, a spring. But if this spring is very powerful then our vehicle might skid.
I searched and found a formula that related the best velocity to go as further as possible :
a_max = μg
- $R$ the radius of a wheel
- $\mu$ the coefficient of friction
- $m$ the mass
- $I$ the moment of inertia
The problem is we are looking for a velocity (without t) to calculate the ratio to transmit to the gear system.
We found the equation for the acceleration but not the velocity, that what we are looking for.