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E. Stays unchanged 12. An object travels in a circular path of radius r at a constant speed v. What happens to the object’s acceleration if the speed is doubled and the radius stays unchanged? A. It doubles B. It quadruples C. It is cut to a half D. It is cut to a quarter E. Stays unchange

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E. Stays unchanged 12. An object travels in a circular path of radius r at a constant speed v. What happens to the object’s acceleration if the speed is doubled and the radius stays unchanged? A. It doubles B. It quadruples C. It is cut to a half D. It is cut to a quarter E. Stays unchange

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Solution

The acceleration of an object moving in a circular path is given by the formula a = v^2/r, where v is the speed of the object and r is the radius of the path.

If the speed is doubled, the new speed will be 2v. Substituting this into the formula gives a = (2v)^2/r = 4v^2/r.

This is four times the original acceleration, so the correct answer is B. It quadruples.

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How does the radius of an object moving in a circular path relate to its acceleration?  If the radius  increases, what happens to the acceleration?

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