Proper velocity by Hermann Minkowski's flat-space metric equation . Here a reference map frame of yardsticks and synchronized clocks define map position x and map time "t" respectively, and the "d" preceding a coordinate means infinitesimal change. A bit of manipulation allows one to show that proper velocity where as usual coordinate velocity . Thus finite "w" ensures that "v" is less than lightspeed "c". By grouping "γ" with v in the expression for relativistic momentum p, proper velocity also extends the Newtonian form of momentum as mass times velocity to high speeds without a need for relativistic mass. The proper velocity
Wheelie to mass times acceleration, then the minimum power required for a wheelie can be expressed as the product of mass, velocity, and the minimum acceleration required for a wheelie: Thus the minimum power required is directly proportional to the mass of the vehicle and to its velocity. The slower a vehicle is moving, the less power is required to perform a wheelie, and that is without even considering the power required to overcome air drag, which increases with the cube of velocity. Therefore, the least amount of power required is when the vehicle begins accelerating from rest. In the case