Velocity squared veurses distance

[enthdegree]

Homework Statement

I've calculated the maximum velocity of a mass at the bottom of a pendulum given various amplitudes. I've also gotten the distance that mass falls from it's angle furthest from the extreme to it's lowest point.
I'm being asked to graph the maximum velocity squared vs the distance traveled for a bunch of increasing amplitudes and then interpret that graph.

The graph appears to be linear but I have no idea what physical value it could represent. We have not yet learned in physics what m^2/t^2 values represent over m. Could it be maximum accelleration>>?

It'd be great if someone could clear this up for me, thanks!

 

[Andrew Mason]

Homework Statement

I've calculated the maximum velocity of a mass at the bottom of a pendulum given various amplitudes. I've also gotten the distance that mass falls from it's angle furthest from the extreme to it's lowest point.
I'm being asked to graph the maximum velocity squared vs the distance traveled for a bunch of increasing amplitudes and then interpret that graph.

The graph appears to be linear but I have no idea what physical value it could represent. We have not yet learned in physics what m^2/t^2 values represent over m. Could it be maximum accelleration>>?

It'd be great if someone could clear this up for me, thanks!

By equating maximum potential energy (v=0) to maximum kinetic energy (h=0) we have:

v^2 = 2gh

where h is the maximum height. So v^2 represents an acceleration x distance (potential energy / unit mass).

AM