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"
Signal velocity if you know any two, you can calculate the rest. In a uniform medium if the permeability is constant, then variation of the signal velocity will be dependent only on variation of the dielectric constant. In a transmission line, signal velocity is the reciprocal of the square root of the capacitance-inductance product, where inductance and capacitance are typically expressed as per-unit length. In circuit boards made of FR-4 material, the signal velocity is typically about six inches (15 cm) per nanosecond. In circuit boards made of Polyimide material, the signal velocity is typically about 16.3 cm per nanosecond or 6.146