Basic Kinematics: Analyzing Distance v Time and Distance v t^2 Graphs

[dauerbach]

Just finished an experiment that seems totally screwed up. We let a roller decend an inclined plane of 7 and 9 degrees respecitvely and let it roll from 25 to 50 cm in increments of 5 cm. We then graphed distance v. time and distance v t^2. I thought the first should be a log scale, the second a straight line, but I couldn't get a good fit. What should these graphs tell me about the motion of the roller? How do I compute the acceleration due to gravity from the GRAPHS?

 

[jmb88korean]

if distance vs time gives you velocity, doing distance vs time gives you velocity, which vs. time gives you acceleration. slope of second graph is acceleration

 

[Paulie323]

I am not positive if this is what you were asking but, to find the acceleration vs time graph just derive the velocity vs time graph this will give you a linear graph of acceleration.

 

[zhermes]

I thought the first should be a log scale, the second a straight line

You're exactly right. The first should be exponential (what simple equation tells you this?), and the second linear.

but I couldn't get a good fit.

This could just be due to bad experimental setup (e.g. weird frictions, timing inaccuracies, etc).

What should these graphs tell me about the motion of the roller? How do I compute the acceleration due to gravity from the GRAPHS?

What should (hypothetically) the slopes of each graph be?