Graphical Analysis: Identifying Greatest Acceleration

[MIA6]

Generally, on a graph that describes motion, position v.s. time, there are several different kind of segments. For example, parabola (not a complete parabola, but partial), or the graph for y=x^(1/2), [since I can't provide image, I can only describe it, so you have to imagine] There are some points labeled on the graph, I know for the greatest velocity, you can see the slope of the graph. But how do you know which labeld point has the greatest magnitude of acceleration?

 

[Omri]

I don't know about the greatest points, but you can distinguish between positive and negative acceleration using convex/concacve considerations. You can than try to estimate minimum and maximum values, according to the graph itself (maybe there's a general method, but I can't think of one right now).

 

[MIA6]

RIght, convex, and concave. Concave is increasing, convex is decreasing. btw, just think of a new question, by looking at convex or concave graphs, how can I know if this is uniform accelerated or not uniform accelerated? it might accelerate 3m/s in the 2nd second, then 5m/s in the third second?

 

[TVP45]

On your position vs time graph, calculate slopes (dy/dx) for, say, every 3rd grid box and wherever it looks like something is happening (the labeled points). Then graph those slopes vs time on the same graph but with a different color. Use a second y scale that keeps the curves near one another. The slope of the second curve is acceleration. If you want, do the slopes of that curve for a third curve. If you use a plastic see-thru ruler, this is an easy technique.

 

[MIA6]

But on a test, I will not be able to do these things. The graph appears in multiple-choice question, so there is no grid box for that.

 

[TVP45]

I hope and pray you are in high school and not a university if you have a multiple choice question about a graphical interpretation. OK, there are two techniques, only one of which is educational. Here is a link that will help a little. http://www.bbc.co.uk/schools/gcsebitesize/physics/forces/speedvelocityaccelerationfhrev2.shtml
and here is another
http://www.shodor.org/interactivate/discussions/GraphingTime.../

Now, the other method: remember that acceleration is a change in velocity. You know velocity is the slope of the distance vs time line, so look at where the slope of the line changes. Imagine yourself walking. When the line is steep, walk fast. When the line is level, stop. And so on. Pay attention to when your speed changes quickly. That is a lot of acceleration.

 

[robphy]

You should associate acceleration with curvature in the position-time graph. This can be made precise... but this isn't the place for that.

A portion of uniformly accelerated motion is a portion of a parabola on the position-time graph.

 

[MIA6]

I hope and pray you are in high school and not a university if you have a multiple choice question about a graphical interpretation. OK, there are two techniques, only one of which is educational. Here is a link that will help a little. http://www.bbc.co.uk/schools/gcsebitesize/physics/forces/speedvelocityaccelerationfhrev2.shtml
and here is another
http://www.shodor.org/interactivate/discussions/GraphingTime.../

Now, the other method: remember that acceleration is a change in velocity. You know velocity is the slope of the distance vs time line, so look at where the slope of the line changes. Imagine yourself walking. When the line is steep, walk fast. When the line is level, stop. And so on. Pay attention to when your speed changes quickly. That is a lot of acceleration.

Yes,I am in high school. Your two websites help me a lot. but btw, when a question asks you on a graph, which point has the greatest acceleration, it means the instantaneous acceleration, right? Instantaneous acceleration means to find the acceleation in a very very short time, approaching to zero, but not equal to zero (according to calculus), if it is zero, then how can a car accelerate at a time of 0? You can't go from 0.5 meters per second to 3 meters per second in no time, it will still take time to accelerate, here i think it is a very short time. So we still have to find two points that are very close to each other conceptually (velocity and time),then divide them to find the acceleration?