Question Number 59104 by Forkum Michael Choungong last updated on 04/May/19
$${i}\:{want}\:{of}\:{ask}\:{in}\:{mechanics}\:{is}\:{this} \\ $$$${possible}?? \\ $$$$ \\ $$$${power}=\frac{{work}\:{done}}{{time}\:{taken}} \\ $$$${if}\:{power}\:=\:{p}_{{w}} \:,\:{Work}=\:{W}_{{d}} ,\:{and}\:{time}={t} \\ $$$$\Rightarrow\:{p}_{{w}} =\:\frac{{W}_{{d}} }{{t}} \\ $$$${but}\:{W}_{{d}} =\:{force}\left({f}\right)×{distance}\left({s}\right) \\ $$$$\:\:\:\:\:\:\:\:{W}_{{d}} =\:{fs} \\ $$$$\Rightarrow\:{p}_{{w}} =\:\frac{{f}×{s}}{{t}} \\ $$$$\:\:\:\:\:{p}_{{w}} =\:{f}\:×\:\frac{{s}}{{t}}\left({distance}/{time}\right) \\ $$$$\:\:\:{p}_{{w}} =\:{f}\:×\:{velocity} \\ $$$$\:\:\:{but}\:{f}={ma} \\ $$$${p}_{{w}} =\:{m}×{a}×{v} \\ $$$${rearranging} \\ $$$$\Rightarrow\:{p}_{{w}\:} =\:{m}×{v}×{a} \\ $$$$\:\:\:\:\:\:{p}_{{w}} =\:{momentum}\left({P}\right)×{Acceleration}\left({a}\right) \\ $$$${Power}\:=\:{momentum}\:×\:{Acceleration}. \\ $$$${the}\:{momentum}\:{of}\:{a}\:{system}\:{is}\:{directly} \\ $$$${propotional}\:{to}\:{the}\:{power}\:{of}\:{that}\:{system} \\ $$$${but}\:{will}\:{have}\:{a}\:{minimum}\:{momentum} \\ $$$${when}\:{accelerating}. \\ $$$$ \\ $$$${what}\:{do}\:{you}\:{think}? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$