Final answer:
The direction of acceleration when an object's velocity changes uniformly from due east to due north is directed toward the northwest, providing the centripetal force required for it to move in a circular path.
Step-by-step explanation:
When the direction of an object's velocity changes uniformly from due east to due north, the acceleration is directed toward the center of the circular path the object would be moving along. This is because acceleration is defined as the change in velocity, which can involve changes in speed, direction, or both. In the case of uniform circular motion, even if the speed is constant, changing direction means there is a centripetal acceleration.
In the scenario where an object's velocity changes from east to north, the direction of the acceleration must be perpendicular to the velocity and toward the center of the circular path of the motion. The acceleration is therefore directed toward the northwest, assuming a two-dimensional plane where east and north are at right angles to each other.
Centripetal acceleration is a key term for this type of motion. It's the acceleration that occurs when an object moves in a circular path at constant speed and is always directed toward the center of the path. As such, when velocity changes direction from east to north, the resulting centripetal acceleration is toward the northwest.