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"
Biomechanics of sprint running ground forces is also very important. Weyand et al. (2000) came up with the following equation for determining sprint velocity: where formula_2 is the sprint velocity (m/s), formula_3the step frequency (1/s), formula_4 the average force applied to the ground (N), formula_5 the body weight (N), and formula_6 the contact length (m). In short, sprint velocity is reliant on three main factors: step frequency (how many steps you can take per second), average vertical force applied to the ground, and contact length (distance your center of mass translates over the course of one contact period). The formula was tested by having