Math Problem Statement
Solution
Let's analyze and answer the two questions based on the graphs provided in the image.
Question 1:
Which graph represents a car that is decreasing in speed?
Analysis:
- A car decreasing in speed implies its velocity (speed) is reducing over time. This is represented by a graph where the slope of the speed vs. time graph decreases, i.e., it shows a downward slope.
- Looking at the graphs:
- Graph A shows speed decreasing over time.
- The others (Graphs B, C, and D) do not show this behavior.
Answer: A. Graph A
Question 2:
Which graph represents a car that is not moving?
Analysis:
- A car not moving means its position or distance does not change with time, which implies a flat, horizontal line on the distance vs. time graph.
- Looking at the graphs:
- Graph B shows a horizontal line in the distance vs. time graph, indicating no movement.
- The others (Graphs A, C, and D) show changes in speed or distance over time.
Answer: B. Graph B
Let me know if you'd like detailed explanations for these answers or have further questions!
Here are 5 questions to expand your understanding:
- How do you identify whether a car is accelerating or decelerating from a speed vs. time graph?
- What would a graph look like for a car moving at a constant speed?
- Can a car have a constant speed but a varying distance vs. time graph? Why or why not?
- How would you represent a car accelerating uniformly on both a speed vs. time graph and a distance vs. time graph?
- Why is it important to understand the relationships between speed, distance, and time in graph interpretation?
Tip: Always check the axes and their labels to understand what type of data the graph represents!
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Math Problem Analysis
Mathematical Concepts
Graph interpretation
Speed vs. Time graphs
Distance vs. Time graphs
Kinematics
Formulas
Slope of Speed vs. Time graph (represents acceleration or deceleration)
Theorems
Concept of uniform motion
Relationship between distance, speed, and time
Suitable Grade Level
Grade 8
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