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I have a general question (not necessarily a homework question) about the concept of related rates in differential calculus.

Most related rates problems present to you a question that generally asks,

Afterxtime has elapsed,

or

Att= __,

what is the rate of change between __ and __?

Suppose I have a related rates problems involving kinematics.

At noon, object A is __units away from object B. Object A is moving in an opposite direction away from object B. Object A is moving at a constant rate of __units and object B is moving at a constant rate of __units.

After 4 hours, what is the rate of change of the distance between object A and B.

I am content with the premise. What captures my interest is the question.

If two objects are both moving opposite one another at aconstantspeed, wouldn't the distance between them be changing at a constant speed as well? Why would the derivative of the distance between the objects with respect to time be different afteranytime?

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# The Concept of Related Rates

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