Test whether constant incline is constant acceleration

[BuhRock]

1. A car rolls down such an incline from rest, starting at different positions on the incline.
If the car coasts distances of .7430036cm, .9169641cm, 2.025999cm, and 1.61088cm, starting from rest each time and requires respective times of 3.5 sec, 7 sec, 7.25 sec, and 7.75 sec, is there evidence that acceleration is constant.
2. s = v0(t) + .5at^2
3. I used that equation for each interval and found 4 accelerations. The respective accelerations were: .12 cm/s^2, .04cm/s^2, .08cm/s^2, .05cm/s^2

I'm not sure how to prove that there is evidence that the acceleration is constant. The accelerations are all close together though.

 

[SammyS]

The accelerations are very different. 0.12 is 4 times 0.04 .

B.T.W.: The 0.04 cm/s² acceleration is 0.037 cm/s² to 2 sig. figs.

 

[BuhRock]

So when is asks if there is evidence that acceleration is constant, how do I need to prove that?

 

[SammyS]

With those data, I would say there is evidence that the acceleration is not constant.

 

[rwisz]

Based on the given information, it does appear that there is evidence that the acceleration is constant. The calculated accelerations for each interval are all relatively close to each other, indicating that the car is experiencing a consistent acceleration regardless of its starting position on the incline. Additionally, the fact that the distances and times are increasing in a proportional manner also supports the idea of constant acceleration.

To further confirm this, we can use the equation provided (s = v0(t) + .5at^2) to calculate the expected distance for each time interval, based on the given acceleration values. If the calculated distances match closely with the actual distances, it would provide stronger evidence for constant acceleration.

Furthermore, we can also plot a graph of distance vs. time for each interval and see if the resulting line is a straight line, which would indicate constant acceleration. If the line is curved, it would suggest non-constant acceleration.

In conclusion, based on the given information and calculations, there is evidence to support the idea that the car experiences constant acceleration while rolling down the incline. However, further analysis and experiments may be needed for a more conclusive answer.