is the derivative of the velocity with respect to time give us the sum of the forces, when the forces as function of the distance?
I know the Acceleration is the derivative of the velocity with respect to time, but I did not understand that the derivative of the velocity with respect to time give us the sum of the forces. Anyone has an idea about this information and how we could write the formula for that.
The derivative of velocity with respect to time is acceleration. Acceleration is related to net force by F=ma. Simply multiply the derivative of velocity with respect to time by the mass, and you'll have the net force.