Angle of total acceleration of an object in circular motion

[TheKShaugh]

Homework Statement

A train slows down as it rounds a sharp horizontal turn, slowing from 90 km/h to 50 km/h in the 15 s that it takes to round the bend. The radius of the curve is 150 m. Compute the total acceleration at the moment the train speed reaches 50 km/h

Homework Equations

a = sqrt[a_t^2 + a_r^2]

The Attempt at a Solution

I have the solution for the total acceleration, I'm just wondering what I am supposed to give the angle relative to in these kinds of problems in general. The answer key gives the angle relative to the final velocity vector, is that a good reference point in general?

 

[Nathanael]

I have the solution for the total acceleration, I'm just wondering what I am supposed to give the angle relative to in these kinds of problems in general. The answer key gives the angle relative to the final velocity vector, is that a good reference point in general?

As long as you specify where your angle is measured from, you should be okay. It doesn't really matter what you measure it from. If they want it measured from a certain spot then a problem will tell you where to measure the angle from. Otherwise it doesn't matter (because saying it's "θ from this" or "Φ from that" could be saying the same thing, even though θ ≠ Φ and "this" ≠ "that").

 

[haruspex]

In the present example, I don't see any other option. There are no geographical directions, and you don't know the angle of the turn. In another question there may be other options, but in that case I would hope the statement of the question would tell you what direction to use as the base.