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"
Jerk (physics) Jerk (physics) In physics, jerk is the rate of change of acceleration; that is, the time derivative of acceleration, and as such the second derivative of velocity, or the third time derivative of position. According to the result of dimensional analysis of jerk, [length/time], the SI units for its magnitude are m/s (or m⋅s); this can also be expressed in standard gravity per second ("g"/s). Jerk is a vector, and (as with "acceleration") there is no distinct term to denote its scalar magnitude (more precisely, its norm, as, e.g., there is "speed" for the norm of the velocity vector). Jerk