The relationship between Vav and Height of a ball rolling down a slope

[zzoldan]

Homework Statement

I have this problem on my physics exam and I hoped you guys could help. The Question is: Why is the relationship between the average velocity and the height of a ball rolling down a slope a square root function?
The slope is 100cm long, the height of the ball at the top of the slope is 30cm and the angle is 17.45 degrees.

Homework Equations

S=1/2at2 + viT
Vav = S/T
Vav = (Vi + Vf) / 2

The Attempt at a Solution

I established that the relation is, in fact, represented by a square root function.
I figured out the rule of the function, by determining that the A/K is.
I just have no idea why this is a square root function...
Is it because the ball reaches its' terminal velocity quicker?
Or because, when the height is smaller, there is a much smaller acceleration, ultimately decreasing the average velocity?
Please Help- My exam is on 12/17/09

Thanks :D

 

[member 553083]

The relationship between the average velocity and the height of a ball rolling down a slope is a square root function because the acceleration of the ball due to gravity decreases as it gets closer to the bottom of the slope. As the ball moves down the slope, its kinetic energy (KE) is converted to potential energy (PE) due to the force of gravity acting upon it. As it gets closer to the bottom of the slope, the PE increases while the KE decreases, resulting in a decrease in the acceleration. This decrease in acceleration results in a decrease in the average velocity of the ball, which can be represented by a square root function.