Uniform acceleration of rolling cart

[jnimagine]

We did a lab, where a cart was rolled down a ramp and a tickertape was attached to the cart as it rolled down. When the cart finished the course of rolling down, a line was drawn across the tape through every sixth dot to show that it is an interval of 0.10s.
Then we had to make 3 graphs: distance - time, average velocity - time, and acceleration - time.
When the displacement was graphed, the graph was a curve. The average velocity was calculated by subtracting the displacement at 0.10s from the displacement of 0.20s then dividing it by 0.10s.
When tangents were drawn on the distance time graph and slopes calculated to find out the instantaneous velocity, the slopes were slightly larger than all the average velocities. It said that the average and the instantaneous velocity must be the same. Why is that?? and what could explain the differences between the two in my result?
Also, what are some reasons why the average velocity - time graph does not pass through zero?
When the average velocity was graphed and a line of best fit was drawn, the slope was caculated to figure out the acceleration. This acceleration was only 6.5m/s^2 instead of 9.8m/s^2. What could be some errors in the lab (not human errors) that could have caused this problem??

If anyone could suggest some explanations to my questions, I would greatly appreciate it. Thank you. :)

 

[Jakell]

Easy question first, why the graph does not pass through zero. it does not pass through zero because you started with a velocity interval between t=0s and t=.1s. The smaller that time interval, the closer you would get to a starting velocity of zero. You could have also held the cart at the top for a few points, then dlet it go. That would get you a line that started at zero then increased.

I do not know offhand why the average and instantaneous velocities would ever be the same in this case. At certain points, with smartly chosen averages you might be able to have them be the same. Also if you took your average speed across a smaller time you would get closer to the instantaneous velocity.

 

[charng]

I can provide some insights into your questions and address the possible errors in your lab.

Firstly, the reason why the average velocity and the instantaneous velocity may not be exactly the same is due to the fact that the average velocity is calculated over a specific time interval (in this case, 0.10s), while the instantaneous velocity is calculated at a specific moment in time. This means that the average velocity takes into account the velocity changes over the entire time interval, while the instantaneous velocity only considers the velocity at a specific point in time. This can explain the slight differences between the two values.

In terms of the differences between the two values on your graph, it is possible that there were some measurement errors or uncertainties in your data. This could be due to factors such as human error in recording the data or the equipment used, as well as external factors like air resistance or imperfections in the rolling cart.

The reason why the average velocity - time graph does not pass through zero is because the cart was already in motion when the experiment started. This means that it had some initial velocity, and even though it was rolling down a ramp, there may have been some friction or other external forces acting on it, causing it to have a non-zero average velocity.

As for the discrepancy between the calculated acceleration (6.5m/s^2) and the expected acceleration (9.8m/s^2), there could be several factors at play. One possible error could be the angle of the ramp not being exactly as expected, which would affect the acceleration of the cart. Another factor could be the friction between the cart and the ramp, which would also affect its acceleration. Additionally, there may have been some measurement errors or uncertainties in your data, as mentioned before.

In conclusion, it is important to carefully consider all possible sources of error when conducting experiments, and to take multiple measurements to minimize these errors. Additionally, it is always helpful to compare your results to expected values and investigate any discrepancies to understand the underlying factors at play.