# Finding acceleration and displacement on a velocity vs time graph

#### xCanx

I have a problem, I did a motion lab in class and we had to observe a cart rolling down a ramp. We did it using the ticker tape. I calculated the average velocity and I got a graph like this.

It's not straight, so I'm confused on how to calculate the acceleration and displacement using this velocity vs. time graph.

If you see that dotted line a drew, I was planning to use that slope for the accel. and the area under neath for displacement. Would this work?

I know there are errors, but I can't change the data.

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#### xCanx

Should I just calculate two different slopes and find the total area underneath the entire graph?

#### JoAuSc

It seems like you know the physics, but you're unsure of what your professor wants, and that you're expecting a single answer for the acceleration, but you're confused because that's not quite what you got.

There are three things you could do:
• Give the accelerations for both before and after t=0.1.
• Give the average acceleration, which would be the change in velocity over the entire run divided by the change in time.
• Give just one of the two, probably the second one, if you think this would be more scientifically valid for what you're trying to do, and present your reasons. Let's say, for example, that you're trying to figure out the acceleration due to gravity. In this experiment, we'll say someone puts the car up on the top of the ramp, and someone else starts a stopwatch. If someone started the stopwatch about 0.3 seconds late, and you just assumed the cart was at x=0 when the stopwatch was at t=0, that would throw into doubt the first part of the graph, but the rest of the graph would remain scientifically valid, in which case I'd present the second value. On the other hand, if the first part of the track were frictionless and someone had spilled honey on the rest of the track, then the first part would be most valid.

If you know what went wrong, go with answer #3. If you don't know what went wrong, I'd recommend you go with answer #1, which gives the most complete answer, unless your professor specifically wants a single number.

#### xCanx

Thank you so much :) Ya, I do know the physics, but I wasn't sure if the way I was doing it would be right (I was going to use #1 intially).

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