hi,

 

Was wondering why velocity is squared in motion formulas - such as in -

 

v = squared root of v (squared)x + v (squared)y as in projectile motion and other formulas of motion which have the variable v squared or the subject v squared.

 

Is it do with accounting for resistance, which is like proportional (somehow) to the speed of the object or something...

It depends on the situation. Sometimes it's because of calculus, and sometimes it's because of geometry.

In the example you have given, with vector components, it's because of the Pythagorean theorem of geometry. The components are part of a right triangle, and the resultant is the hypotenuse.

If a velocity has horizontal and vertical components v_x and v_y, then you can think of the object travelling those distances in the x and y directions every unit time, there should be a right angle between them hence the total distance being the hypotenuse of the right angled triangle.