Determine the acceleration of a cart on a track

Your goal in this experiment is to determine the acceleration of a cart as it rolls down a tilted track.

Last time, you measured the time it took a cart to roll certain distances down a tilted track. Today, you must analyze a similar motion in a different way.

Below are a set of measurements I made of the motion of a cart down a ramp. You will note that I did a more careful job this time; the uncertainties in the measurements are all much smaller.


# Time      Distance  Uncert_dist
# (s)        (cm)      (cm)
#---------------------------------------------
0.5        7.0         1.1

1.0       25.1         2.3

1.5       58.2         3.2

2.0      101.1         4.2

2.5      157.6         5.3

3.0      230.2         6.3

3.5      315.5         7.2
#---------------------------------------------

download file "cart_example.dat" if you wish

Use your measurements to make a graph which corresponds to the following equation:

What is the acceleration of the cart? Be sure to include both a value and an uncertainty.

How can you determine the uncertainty in a slope?

Each group must submit via myCourses Assignments a single spreadsheet (or PDF, or materials in other format) showing

the names of all group members, and the group name
a graph showing distance rolled as a function of time SQUARED, together with the best, min, and max slopes
a calculation of the acceleration of the cart; be sure to include units and an uncertainty

If you have time: Is there any way to compute this acceleration, theoretically? If so, how does the theoretical acceleration compare to your measured value?