Variable-mass system events. The following derivation is for a body that is gaining mass (accretion). A body of time-varying mass "m" moves at a velocity v at an initial time "t". In the same instant, a particle of mass dm moves with velocity u. The initial momentum can be written as Now at a time "t" + d"t", let both the main body and the particle accrete into a body of velocity v + dv. Thus the new momentum of the system can be written as Since d"m"dv is the product of two small values, it can be ignored, meaning during d"t"
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