Consider a car driven along a circular racetrack of radius 1.6 km. What is the magnitude of its displacement after 2.5 laps? What is the total distance traveled?

Answer 1

#"3.2 km"#

A circular track of radius #"1.6 km"# has a diameter of #"3.2 km"# (#D = 2r#) and a circumference (distance around) of #"10.05 km"#. (#C = pi xx D#)

After one lap, you're back where you started, so there's no displacement because displacement is a vector quantity, meaning it requires both magnitude (size) and direction away from the original position.

After two laps, it remains the same.

The next half a lap takes the car to the exact opposite side of the track, or one diameter from its start position, #"3.2 km"# away.
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Answer 2

The magnitude of its displacement after 2.5 laps is 0 km. The total distance traveled is (2.5 \times 2 \times \pi \times 1.6 \text{ km} = 8 \pi \text{ km} ) or approximately 25.13 km.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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