@agent0smith The 3 main kinetic equations in basic physics. Do they all derive from each other?

Question

@agent0smith The 3 main kinetic equations in basic physics.  Do they all derive from each other?

raffle_snaffle · Answer

Yes

raffle_snaffle · Answer

You mean kinematics?

agent0smith · Answer

They're derived with calculus starting with $ a(t) = a$ (for constant acceleration). The v^2 = vo^2 + 2a(x-xo) comes from combining a couple of them.

raffle_snaffle · Answer

If you want I can show you Fibchic.

fibonaccichick666 · Answer

Could you @raffle_snaffle ?  I would like to see it.  Or just give me a start.  I can go from the basic start probably.  I thought it was something like $$v_{avg}=\frac{v_f-v_0}{2}$$ then doing something to get $$v_f^2=v_0^2+2ax$$

agent0smith · Answer

Integrating $a(t) = a$ twice gives the below equations. To get $\large v_f^2=v_o^2+2a(x_f-x_o)$...

$\Large v_f=v_o + at$ <=== solve for t

$\Large x_f =x_o+ v_o t + \frac{ 1 }{ 2 }at^2 $ <=== substitute it for t in here

Simplify and you'll have that equation.

fibonaccichick666 · Answer

ah, I meant isn't there another way other than the integration. I remember my physics teacher doing some sort of algebraic manipulation.  The calc version isn't bad

agent0smith · Answer

To get what exactly?