Math Problem Statement
Solution
Let's analyze the image and break down the problem step by step.
Path C (shown in red) involves motion on the displacement axis (x-axis). From the figure:
- Path C starts at ,
- It travels to ,
- Then it turns back to .
We can now address the questions:
(a) The distance traveled (in m):
- Distance is the total path length covered, regardless of direction.
- From to (forward) → ,
- From back to (backward) → .
So, total distance = .
(b) The magnitude of the displacement (in m) from start to finish:
- Displacement is the shortest straight-line distance between the starting and ending points.
- Path C starts at and ends at .
So, displacement = .
(c) The displacement (in m) from start to finish:
- Displacement includes the direction. Since the movement is to the right (positive x-direction), the displacement is:
- .
Summary:
- (a) Distance traveled = ,
- (b) Magnitude of displacement = ,
- (c) Displacement = .
Would you like more details on any step? Let me know if you have any questions!
Here are 5 related questions:
- What is the difference between distance and displacement?
- How does reversing direction affect the total distance but not the displacement?
- Can displacement ever be larger than the total distance?
- How is velocity related to displacement?
- What is the significance of the positive and negative signs in displacement?
Tip: In physics, distance is a scalar quantity (only magnitude), while displacement is a vector (magnitude and direction).
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Math Problem Analysis
Mathematical Concepts
Displacement
Distance
Motion in One Dimension
Formulas
Distance = Total path length covered
Displacement = Final position - Initial position
Theorems
Concept of displacement as a vector and distance as a scalar
Suitable Grade Level
Grades 9-12
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