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Physics / Classical Mechanics 0 / Chapter 2 / Problem 2.25

Classical Mechanics | 0th Edition | ISBN: 9781891389221 | Authors: John R Taylor

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Consider the cyclist of Section 2.4, coasting to a halt

Chapter 2, Problem 2.25

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QUESTION:

Consider the cyclist of Section 2.4, coasting to a halt under the influence of a quadratic drag force. Derive in detail the results (2.49) and (2.51) for her velocity and position, and verify that the constant r = m/cvo is indeed a time.

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QUESTION:

Consider the cyclist of Section 2.4, coasting to a halt under the influence of a quadratic drag force. Derive in detail the results (2.49) and (2.51) for her velocity and position, and verify that the constant r = m/cvo is indeed a time.

ANSWER:

Step 1 of 6

Consider a cyclist is moving with velocity .

Let the mass of cyclist is m

As the cycle is well lubricated and tires well inflated, therefore we can ignore ordinary friction and except at very low speeds, air resistance is purely quadratic.

The air resistance is

Then equation of motion will be as follows:

Now variables are separable so we can integrate on both sides to get

Let the initial velocity of cycle at is and at time let it be

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