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Variables

torque/rpm

gear ratio

Constants

distance object travels

mass of object

motor input

to make it simple i am only using one gear, the motor shaft

acceleration of object = (f/m - 9.8)

velocity of string = RPM x pie x motor shaft diameter

assuming initial v=0,

the derivative of (f/m - 9.8)=RPM x Pie x Shaft diameter

i am trying to find a correlation between the average velocity the object takes to cross a given distance and the shaft diameter (gear ratio), im guessing its a parabola, but how can i do this? plz help thnx