Math Problem Statement
Solution
Let's analyze the graph and address each part of the question systematically:
Part (a) - Find the velocity at specific times:
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At : From the graph, the velocity at is around .
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At : From the graph, the velocity at is around .
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At : From the graph, the velocity at is .
Part (b) - Describe what is happening in the first 2 seconds:
- From to , the velocity of the particle is decreasing linearly, going from at to at . This suggests the particle is slowing down during this time.
Part (c) - When is the particle stationary?
- The particle is stationary when the velocity is . This occurs at:
- seconds and seconds.
Part (d) - Describe what happens when :
- When the velocity is , the particle is momentarily at rest. This happens at and , likely indicating a change in the direction of motion after these points.
Part (e) - When is the velocity increasing?
- The velocity is increasing:
- From to (velocity increases from to ).
Part (f) - When is the velocity constant?
- The velocity is constant:
- From to (velocity is ).
Part (g) - When is the particle moving in a positive direction?
- The particle is moving in the positive direction when the velocity is positive (above the x-axis):
- From to , and from to .
Part (h) - When is the particle moving in a negative direction?
- The particle is moving in the negative direction when the velocity is negative (below the x-axis):
- From to .
Would you like more detailed explanations or further clarification? Here are five related questions for deeper understanding:
- How can you calculate the total displacement of the particle over the given time period?
- What does the slope of the velocity graph represent physically?
- How can you find the total distance traveled by the particle?
- How does the acceleration change during the different time intervals?
- Can you determine the particle’s average velocity over the entire time interval?
Tip:
Always check whether the velocity graph crosses the time axis to identify when the particle changes direction.
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Math Problem Analysis
Mathematical Concepts
Kinematics
Velocity-Time Graph
Linear Motion
Formulas
Velocity = Displacement/Time
Acceleration = Change in Velocity/Time
Theorems
First Equation of Motion (v = u + at)
Graphical Interpretation of Motion
Suitable Grade Level
Grades 9-12
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