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Chapter 2: Problem 11

Consider three ice skaters: Anna moves in the positive \(x\) -direction without reversing. Bertha moves in the negative \(x\) -direction without reversing. Christine moves in the positive \(x\) -direction and then reverses the direction of her motion. For which of these skaters is the magnitude of the average velocity smaller than the average speed over some time interval?

Short Answer

Expert verified
Answer: Christine

Step by step solution

01

Determine the average speed and average velocity for Anna

Since Anna moves in the positive x-direction without reversing, her motion is always in the same direction. This means that her total distance traveled and displacement will have the same magnitude. Therefore, her average speed and average velocity will have the same magnitude.
02

Determine the average speed and average velocity for Bertha

Similarly, Bertha moves in the negative x-direction without reversing, which means her motion is always in the same direction. Just like Anna, Bertha's total distance traveled and displacement will have the same magnitude, so her average speed and average velocity will also have the same magnitude.
03

Determine the average speed and average velocity for Christine

Christine moves in the positive x-direction and then reverses the direction of her motion. This means that her displacement will be different from her total distance traveled as she would be moving in opposite directions. Since the total distance traveled will be greater than the magnitude of the displacement, her average speed will be greater than the magnitude of the average velocity.
04

Conclusion

Therefore, the only ice skater who has the magnitude of her average velocity smaller than her average speed over some time interval is Christine.

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