# Taking force, mass and length as base units, find the dimensional formula of velocity [closed]

My doubt is that how can force be considered as a base quantity. Is that possible? How can I represent the dimension of velocity using it?

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## closed as off-topic by John Rennie, Brandon Enright, jinawee, DavePhD, Kyle KanosMay 14 '14 at 13:02

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You are missing time. Try to write Force in terms of mass, length and time and get units of time from the equation. Put it in that of speed.

You can use any unit that has time to substitute it. But we generally tend to use basic units as fundamental units. The best example is that of current. Although current is rate of flow of charge and charge is more fundamental than current, we use current as base unit because we are comfortable measuring it.

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$$\text{velocity} = \text{length}/\text{time}$$

As you already have length you just need to get time to substitute into the above equation.

Lets examine the formula $F=ma$ to find a dependance between the given base units and the one we are searching for. Breaking down it is: $$\text{Force}=\text{mass}\times(\text{length}/\text{time}^2)$$ Which allows us to solve for time and substitute into the velocity formula.

As for why force can be used as a base unit, I believe (someone please correct me if I'm wrong) any units can b eused as base units. We just happen to use Mass,Length,Time,Current,Temperature,etc. as our base system because it feels most natural to us. Moreover historically people were always aware of "time" and "length" but the notion of a force as we know it was introduced later on.

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