The kinetic energy formula for lagrange doesnt make sense

[grandpa2390]

Homework Statement

This is a real basic question I am sure. Maybe I just missed something.
so in the book, t = the kinetic energy . only for a pendulum, they add kinetic energy of x dot squared, plus kinetic energy of y dot squared.

Homework Equations

T = 1/2 m v^2
a^2 + b^2 = c^2

The Attempt at a Solution

This doesn't make sense. At first I thought maybe they were splitting velocity into x and y components.
but T(velocity) is not equal to T(x component of velocity) + T(y component of velocity). if I am traveling in a straight line at 5 m/s, 1/2m(5)^2 is not equal to 1/2m(3)^2 + 1/2m(4)^2. what is the xdot and ydot a measure of

 

[haruspex]

1/2m(5)^2 is not equal to 1/2m(3)^2 + 1/2m(4)^2

Are you a betting man?

 

[grandpa2390]

Are you a betting man?

No I am not. And I get the feeling you are about to tell me that it's a good thing. lol because 3^2 +4^2 does equal 5^2 ... this is what I get for forcing myself out of bed to study... sry for the inconvenience. It made sense earlier when I was awake. Then I take a nap. force myself up, and I am writing a formula that says exactly what I said wasn't making sense. lol.

They only hope I have to hold onto is that my professor says that you aren't a physicist unless you occasionally write something stupid.

edit: I know what i was thinking. the variable itself v being plugged in, and then just replacing it with components added. x and y. 3 + 4 != 5 but i guess that's why v is squared in kinetic energy. so that the kinetic energy of components can be added. you can't say .5m(x+y)^2 but u can say the other