A roller coaster cart travelling due north at 20m/s that turns left during an interval of 4.0s without changing speed. Find the average acceleration.

I understand the mathematics behind it (using pythagoras's theorem to find velocity and the formula acceleration = velocity/time) BUT I don't understand how to find the direction.

The answer in my text book says south west, but intuitively that just doesn't make sense if you draw out the path taken. Can anyone explain how the direction is south west?

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  1. Draw a vector from the origin pointing
    due north. Then draw a vector from the
    origin pointing due west. Since the 2 vectors are equal, the resultant vector
    will fall midway between them(135o or
    North West). Mathematically:

    tanAr = Y/X = 20/-20 = -1.0
    Ar = -45o = Reference angle.
    A = -45 + 180 = 135o, North West.

    If we change the North bound vector to due South, then the direction would
    be South West.

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