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A circular test track for cars has a circumference of 4.7 km. A car travels around the track from the southernmost point to the northernmost point. What distance does the car travel? What is the car's displacement from its original position?

2 Answers

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Final answer:

The distance a car travels from the southernmost to the northernmost point on a circular track with a circumference of 4.7 km is 2.35 km, which is half of the circumference. The displacement, being the straight-line distance between the starting and the ending points, is approximately 1.50 km, calculated from the track's diameter.

Step-by-step explanation:

To answer how far a car travels from the southernmost to the northernmost point on a circular track with a circumference of 4.7 km, it is important to understand the difference between distance and displacement.

The distance refers to the actual path length traveled by the car. Since the track is circular, and the car is going from the southernmost point to the northernmost point, it traverses half of the circumference. Therefore, the distance traveled is half of 4.7 km, which is 2.35 km.

Displacement, on the other hand, measures the straight-line distance from the starting position to the final position, regardless of the path taken. On a circular track, this would be the diameter of the circle. Since the circumference is 4.7 km, using the circumference formula C = pi*d, we find that the diameter d is 4.7 km / pi. Using 3.14159 as an approximation for pi, the displacement is approximately 1.50 km.

The car's displacement from its original position is therefore half the circumference as its straight-line distance through the center of the track, while the distance it actually drives is half the track's circumference.

User Tong
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Well, for the distance traveled, the car goes from the northernmost point to the southernmost point. So, it travels half of the circle's circumference = 4.7/2 = 2.35 km.

For the displacement, by going from the northernmost point to the southernmost point, the car basically just travels the diameter of circle.

So, using the formula: Circumference = 2πr = πd

Hence, the d = C/π = 4.7/π = 1.49605... = 1.5 km (2 significant figures)
Therefore, displacement = 1.5 km
User Snehasish Karmakar
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