I need to prove that force is proportional to acceleration given the results of my experiment. We used a frictionless air glide track at a fixed angle and took data on the velocity of a gliding flag moving down the track. In the experiment, I put more weight on the flag for each successive trial, yet the measured final velocity for each trial was the same, at around 0.4 m/s. So for each trial at a fixed angle, I got the exact same velocity for all runs, despite the change in weight put on the flag. Given this data, I'm supposed to prove that force is proportional to acceleration
a=[v(final)^2-v(initial)^2]/(2x) <-----x is the distance travelled, and v(initial) is 0
The Attempt at a Solution
The best I could come up with was that acceleration was fixed because force and mass were in the same ratio for each trial, but force must've increased for each trial along with the increase in mass to keep acceleration fixed. I'm not sure how a fixed acceleration with an increasing force can show how force and acceleration are proportional.
If you all need more information just let me know, and I may be able to provide it since I have more information from the experiment.
I would appreciate the help!