Exploring Displacement and Average Velocity: Kinematic Equation

[vinnie4]

This question is part of a lab report I've been working on, sorry in advance if I didn't follow all guidelines here.
1. Homework Statement
Explain what the shape of the graph tells you about the mathematical relationship between displacement and average velocity. Include the kinematic equation that correctly relates initial velocity, final velocity, acceleration and displacement.

Homework Equations

v^2 = v_o^2 + 2a($$\Delta$$ x)

3. The Attempt at a Solution
I've already done the graph which is a half parabolic shape with displacement on the y-axis and average velocity on the x-axis (i know the independent variable should be on the x, but my teacher wanted us to graph it this way to see the parabola). I also understand that the velocity increase starts out at a slower rate than the increase in displacement, but after a certain point, the velocity increases at a higher rate than the displacement.

Is that it or am i missing something else?
Also, could someone help me word it in a neater fashion?

 

[jbsteele]

This shape tells us that the mathematical relationship between displacement and average velocity follows the kinematic equation: v^2 = v_o^2 + 2a(\Delta x). This equation relates initial velocity, final velocity, acceleration and displacement, where v is the final velocity, v_o is the initial velocity, a is the acceleration, and \Delta x is the displacement. The graph demonstrates that the rate of increase in velocity starts out lower than the rate of increase in displacement, but eventually accelerates until it increases at a higher rate than displacement.