Why Does Distance vs. Velocity Create a Parabolic Graph?

[lawk]

Homework Statement

Why is a parabola formed when a graph of distance(y axis) vs. velocity(x axis) is plotted against each other? (constant acceleration)

Homework Equations

s=ut+1/2at^2 (guessing?)
v^2-u^2 = 2as (guessing?)

The Attempt at a Solution

I don't know if there is any relationship between veloctiy and distance without knowing the time. But my teacher told me that time was not needed to prove it was a power function...?

 

[Ekpyrotic]

Hi.

I'd say you're thinking about the problem in the wrong way.

Try drawing up the parabolic graph of distance vs velocity, and then ask yourself what the graph's shape is suggesting.

I hope that's a good enough hint in the right direction.

~ Ek.

 

[lawk]

I don't really understand...
my data is like below
distance(m)
1
1.3
1.5
1.69
vel(m/s)
1.1675
1.325
1.4275
1.51

How can I prove what kind of function is it??

The graph looks like this...