Why Do Phys Equations Use Squared Signs?

[majormuss]

Hi guys,
I have a question : why do some equations in Physics have a square sign. For example in the Centripetal Acceleration formula v(squared)/radius, Coulombs law, q(1)q(2)/distance(squared).
Can u explain it in a way that helps me understand the way formulae are discovered .

 

[Borek]

Initially it was just discovered experimentally - for example, if you take two charged objects and you measure force between them, then you move them apart so that distance doubles - force gets four times smaller. You move them further, so that distance triples - and force goes down to one nineth of the original. That means force scales with the reciprocal of distance squared.

 

[sweet springs]

Hi.
Each square has proper meaning or interprtation, e.g.
Coulombs law, q(1)q(2)/distance(squared).: distance(squared) means surface area of the sphere centered at the charge.
the Centripetal Acceleration formula v(squared)/radius : positive, so centripetal for any direction of v. Kinetic energy 1/2 m v^2 is another example.

Regards.