Question
Suppose the velocity of an object moving along a line is positive. Are position, displacement, and distance traveled equal? Explain. Choose the correct answer below. A. Yes, if the velocity is positive then the displacement, distance traveled, and position of the object will be given by \( v^{\prime}(t) \). B. No, the displacement and distance traveled by the object will be equal but since the initial position is not given, the position of the object may not be equal to the distance traveled and the displacement of the object. C. No, the displacement and position of the object will be equal but since the initial position is not given, the distance traveled by the object may not be equal to the position and the displacement of the object. D. Yes, if the velocity is positive then the displacement, distance traveled, and position of the object will be given by \( \int_{\mathrm{a}} \mathrm{v}(\mathrm{t}) \) dt.
Ask by Mckenzie Barber. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
**Answer:**
**B.** No, displacement and distance traveled are equal, but without knowing the initial position, the object's position may not be equal to these quantities.
**Explanation:**
When an object moves with constant positive velocity along a straight line:
- **Displacement** and **distance traveled** are the same because the object moves in one direction.
- **Position** depends on where the object started. Without knowing the initial position, we can't say the object's position is equal to the distance traveled or displacement.
So, displacement and distance traveled are equal, but the object's position may not be equal to these unless the initial position is known.
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Bonus Knowledge
The correct answer is B. No, the displacement and distance traveled by the object will be equal but since the initial position is not given, the position of the object may not be equal to the distance traveled and the displacement of the object. When an object moves with positive velocity, displacement (change in position) and distance traveled (total ground covered) are indeed the same. However, position refers to the object's location at a particular time, which can vary based on the initial position set relative to an origin.
