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.