A car travels 3 miles north, 6 miles south, 2 miles east, 2 miles west, and then 3 miles north. Which of the following is true?

Question

A car travels 3 miles north, 6 miles south, 2 miles east, 2 miles west, and then 3 miles north. Which of the following is true??  
A. The displacement of the car is 16 miles, and the distance traveled is 0 miles.  
B. The displacement of the car is 16 miles, and the distance traveled is 16 miles.  
C. The displacement of the car is 0 miles, and the distance traveled is 0 miles.  
D. The displacement of the car is 0 miles, and the distance traveled is 16 miles.

Accepted Answer

Correct Answer: (D)The displacement of the car is 0 miles, and the distance traveled is 16 miles.. 
Rationale: The displacement of the car is 0 miles, and the distance traveled is 16 miles. After moving north, south, east, west, and north again in the specified amounts, the car returns precisely to its starting point, resulting in zero net displacement, while the total path length sums to 16 miles.A) The displacement of the car is 16 miles, and the distance traveled is 0 milesThis reverses the definitions: distance cannot be zero if the car moved, and displacement cannot exceed the total path length. This scenario is physically impossible.B) The displacement of the car is 16 miles, and the distance traveled is 16 milesThis would only occur if the car moved in a straight line without changing direction. Here, opposing motions cancel out, so displacement is not equal to distance.C) The displacement of the car is 0 miles, and the distance traveled is 0 milesWhile the displacement is indeed zero, the car clearly traveled a cumulative distance of 3 + 6 + 2 + 2 + 3 = 16 miles. Distance is never zero when motion has occurred.D) The displacement of the car is 0 miles, and the distance traveled is 16 milesThis is correct. The north-south movements (+3 – 6 + 3) sum to zero, and the east-west movements (+2 – 2) also cancel. The car ends where it began, so displacement is zero, but the total distance covered is 16 miles.ConclusionDisplacement depends only on initial and final positions, while distance depends on the entire path. The car returns to its origin, so the correct answer is D) The displacement of the car is 0 miles, and the distance traveled is 16 miles.

A car travels 3 miles north, 6 miles south, 2 miles east, 2 miles west, and then 3 miles north. Which of the following is true?

The displacement of the car is 0 miles, and the distance traveled is 16 miles.

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