Why Are Instantaneous and Average Velocities Different in Uniform Acceleration?

[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. :)

 

[qspeechc]

What said that the average- and instantaneous- velocities should be the same? Maybe "it" meant they should be roughly the same.

Also, what are some reasons why the average velocity - time graph does not pass through zero?

Possible because you are using average velocity, and not instantaneous. Maybe you chose t=0 to be some point on the tape that was actually after you started the cart rolling. It could be innacurate drawing, or measuring.

The reason the acceleration came out as it did could be as a result of friction, wonky cart, maybe the tape was pulling on the cart and slowing it, bad drawing, measuring etc.

 

[Moetasim]

I would like to commend you on your thorough and detailed lab report. It seems like you have a good understanding of the concepts and procedures involved in this experiment. I would be happy to provide some explanations and suggestions for your questions and concerns.

Firstly, the fact that the displacement-time graph is a curve is expected. This is because the cart is undergoing uniform acceleration, which means its velocity is changing at a constant rate. This results in a curved graph, as opposed to a straight line for constant velocity.

Regarding the difference between average and instantaneous velocity, it is important to understand that average velocity is calculated over a specific time interval, while instantaneous velocity represents the velocity at a specific moment in time. So, while the average velocity may be close to the instantaneous velocity at a given time, they may not always be exactly the same. This could be due to slight variations in the cart's acceleration or other factors.

As for why the average velocity-time graph does not pass through zero, this could be due to the initial velocity of the cart before it started rolling down the ramp. If the cart was already moving at a constant velocity before the experiment, this would result in a non-zero average velocity at the beginning of the experiment.

In terms of the discrepancy between the calculated acceleration (6.5m/s^2) and the expected acceleration (9.8m/s^2), there could be a few possible reasons. One possibility is that there were some systematic errors in the experiment, such as friction or air resistance, that affected the acceleration of the cart. Another possibility is that there were some errors in the measurements or calculations, which could be addressed by repeating the experiment and taking more precise measurements.

Overall, it is important to keep in mind that experiments are not always perfect and there can be various factors that affect the results. It is important to carefully consider and analyze all the data and possible sources of error to come to a conclusion. I hope this helps to answer your questions and address your concerns. Keep up the good work in your scientific endeavors!