Math Problem Statement
What is the acceleration at 8 seconds
Solution
To determine the acceleration at 8 seconds, we need to analyze the velocity vs. time graph. Acceleration is the rate of change of velocity, so it can be found by calculating the slope of the velocity-time graph.
Let's break it down:
- At 8 seconds, the graph shows the velocity to be around -3 m/s.
- Between 6 and 9 seconds, the velocity changes from 0 m/s to -4 m/s.
The slope (acceleration) over this period is calculated by:
Thus, the acceleration at 8 seconds is:
Would you like further details or explanations?
Here are 5 related questions:
- What is the total displacement during the 9-second interval?
- How would you calculate the average velocity over the entire interval?
- What is the object's position at 9 seconds if it started at 10 m?
- How would you describe the motion from 2 to 5 seconds?
- Can you determine the maximum acceleration in the graph?
Tip: Remember, in a velocity-time graph, the slope at any point gives the acceleration!
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Math Problem Analysis
Mathematical Concepts
Kinematics
Acceleration
Velocity-Time Graph
Formulas
Acceleration = (Change in velocity) / (Change in time)
Theorems
Slope of velocity-time graph gives acceleration
Suitable Grade Level
Grades 9-12
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