Math Problem Statement
Solution
The problem is as follows:
The motion of a material point is given by the function on the interval . The graph of , which represents the velocity of the point, is shown in Figure 279. You are tasked to determine the moment in time when the velocity of the point is equal to .
Solution:
- The graph represents the velocity of the point. From the graph in Figure 279, we need to find the time where .
- Observing the graph:
- At , the velocity .
- This is the only time on the graph where .
Answer:
The moment in time when the velocity of the point is equal to is seconds.
Would you like a detailed explanation of the graph analysis or additional related concepts?
Here are five follow-up questions to deepen your understanding:
- What is the significance of the derivative in motion-related problems?
- How can you determine acceleration using this graph?
- What does the area under the curve represent in terms of the original function ?
- How would you find when the velocity is negative using this graph?
- How does this graph relate to real-world motion problems?
Tip: Always identify key values (like maxima, minima, or specific points) directly on a graph to quickly locate critical information.
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Math Problem Analysis
Mathematical Concepts
Derivative
Velocity in motion
Graph interpretation
Formulas
S'(t): The derivative of displacement function represents velocity
Theorems
Fundamental Theorem of Calculus
Suitable Grade Level
Grades 9-12
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