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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.

Tony
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  • The derivative will give you acceleration, and F=ma so you need to times the derivative of velocity by the mass to get the sum of forces – inspd Sep 25 '15 at 08:49

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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.

Nuclear Hoagie
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  • Many thanks Matt and Inspd for your help, but do you mean the net force can be written in this formula $F=m a$. And is it correct if I want to find the mass I use $m=\frac{F}{a}$ – Tony Sep 25 '15 at 09:14
  • Yes, F represents the net force (i.e. the sum of all forces). If you know the net force and the acceleration, you can use that formula to find the mass. – Nuclear Hoagie Sep 25 '15 at 09:15
  • Many thanks Matt that very helpful. – Tony Sep 25 '15 at 09:24