Why is the slope of a V2 Vs. X Graph 2a?

[YungEggy]

I just need to know what equations and everything is used to explain why the slope of V2 Vs. X graph is 2a. I understand why V vs. T is a and X vs T2 is 1/2a.
Thanks!

 

[fss]

a = v/t (velocity vs. time)

x = (1/2) a t² -> x / t² = (1/2) a (x vs. t² is a/2)

v_f² = v_i² + 2 a x

If v_i² = 0, you can rearrange the above equation to get the slope of the v_f² vs. x graph similar to the way you got the slope of the x / t² graph.

 

[YungEggy]

But the only problem I have is where did the 2 come from? I understand how to arrange it to get the slope of a postion time graph.

 

[paragchitnis]

But the only problem I have is where did the 2 come from?

Which 2? vf² = vi² + 2 a x This one?

Multiply the equation vf = vi + at with itself
vf² = vi² + a²t² + 2atvi
vf² = vi² + 2a( vit + at²/2)
vf² = vi² + 2ax