Math Problem Statement
Solution
The graph you provided displays the velocity versus time for a particle, and the question asks for the particle's acceleration at .
To determine acceleration:
- Acceleration is the rate of change of velocity with respect to time, defined as .
- In this case, the graph shows a linear relationship, meaning that the slope of the velocity-time graph represents the constant acceleration.
Step-by-step solution:
-
Identify points from the graph:
- At , the velocity .
- At , the velocity .
-
Calculate the slope of the line (acceleration): The slope of the line is: Using the points and :
Result:
The acceleration is constant throughout the time interval, so at , the particle's acceleration is:
Would you like further details or have any questions? Here are some related questions you could explore:
- What would be the particle's velocity at ?
- How far has the particle traveled by ?
- What is the particle's displacement during the entire 3-second interval?
- What would happen to the motion if the acceleration was positive instead of negative?
- Can we calculate the average velocity of the particle between and ?
Tip: In velocity-time graphs, the slope gives you acceleration, and the area under the curve gives you displacement.
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Math Problem Analysis
Mathematical Concepts
Kinematics
Velocity-Time Graphs
Acceleration
Formulas
a = Δv / Δt
Theorems
Slope of Velocity-Time Graph
Suitable Grade Level
Grades 9-12
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