How Should You Calculate Roller Coaster Acceleration Using Motion Diagrams?

[Glorzifen]

Homework Statement

Homework Equations

a=(v2-v1)/t

The Attempt at a Solution

I used the vector between the point before A and A as my v2.
I used the vector between the point two before A and the point before A as my v1.
I put them tail to tail and he resultant vector looks like (E) in the image.

Is this how I'm supposed to do these problems?

 

[JaWiB]

Roughly, yes. The problem is poorly worded because the average acceleration "at" A is confusing. "Average" implies either a finite time interval or a set of values, but "at" implies a single point or instant. I would have either asked for the instantaneous acceleration or asked for the average acceleration between two points.

If you have a start and end point on the path, then you can find the direction of the initial and final velocities (v1 and v2) by drawing the tangent line at those two points, and your average acceleration will point in the direction given by the vector difference v2 - v1

If you want to approximate the instantaneous acceleration, you can simply choose two points very near to A (on either side of it) and follow the same method; the closer those points are to A, the better approximation it gives. It sounds like this is what you did, but by choosing two points that were already marked for you.