Answer:
22.6° west of north
Explanation:
Given the velocity of a car changes from 5 m/s east to 10 m/s north after 2 seconds, you want to know the direction of the acceleration.
Acceleration
The acceleration is the rate of change of velocity. The average acceleration will be the ratio of the difference in velocity to the corresponding difference in time.
The difference between ending and starting velocity in (east, north) coordinates is ...
(0, 12) -(5, 0) = (-5, 12) . . . . . . m/s
This represents a 2nd-quadrant direction of ...
arctan(-12/5) = 180° -67.4° = 112.6° . . . . . CCW from east
The direction of the acceleration is 22.6° west of north.
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Additional comment
In the attachment, the angles are measured CW from north, so -22.6° represents an angle 22.6° west of north. We find this representation of direction angles works well with navigation problems that reference cardinal directions.
In the above angle computation, we could also say the angle is 67.4° north of west. This is a less conventional way to represent navigation angles.
