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Can a car that has been traveling at different speeds in a straight line east have accelerated west?
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Every time the car slows down, it is accelerating in the opposite direction the car is travelling. So yes, the car is accelerating west at some points of the trip.
From the wording of the question, yes. The key word is "different speed", so we assume any pair of relative speeds is possible (faster then slower, slower then faster). So if the car went faster and then slower, a deceleration must have occured. A deceleration is an acceleration in the opposite direction.
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