Time Reversal

A movie is made showing successive frames for an object accelerating downward. If the sequence is run backward, the object accelerates (a) upward or (b) downward. Explain.

Answer

Answer b: the acceleration is still downward. The reversed motion is upward, but the object is decreasing its speed because the acceleration is downward. A good example of this behavior is the flight of a ball tossed upward. At all moments the acceleration is downward, toward Earth’s center. Yet the ball moves upward with decreasing speed, turns around, and moves downward. Even at the turnaround point its acceleration is downward.

Quite often people become confused between velocity and acceleration. They are two different vector quantities that should be separated conceptually, but they are mathematically related. Their directions can be the same or opposite along the line of motion. Newton’s second law relates forces and accelerations but says nothing about velocities, for example. And we know that Aristotle was wrong when he proposed that a force was required to keep an object moving. The real world operates with just the opposite rule because no net force is required to keep an object moving in a straight line at a constant speed!

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