velocity

[1123581321]

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...

[ydoaPs]

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

[swansont]

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.

[the tree]

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.