Math Problem Statement
Solution
Let's analyze the provided graph and solve the questions.
Graph Interpretation
- The graph represents velocity (v) in km/h as a function of time (t) in minutes.
- Key points:
- From to min, the velocity increases from 0 to 45 km/h.
- From to min, the velocity remains constant at 45 km/h.
- From to min, the velocity increases to 75 km/h.
- From to min, the velocity remains constant at 75 km/h.
- From to min, the velocity decreases to 0 km/h.
(a) Sketch of Acceleration and Distance Graphs
-
Acceleration Graph:
- Acceleration is the change in velocity over time.
- From to min: The car accelerates from 0 to 45 km/h. The slope indicates positive acceleration.
- From to min: No change in velocity, so acceleration is 0.
- From to min: The velocity increases from 45 to 75 km/h, indicating positive acceleration.
- From to min: No change in velocity, so acceleration is 0.
- From to min: The car decelerates to 0 km/h, showing negative acceleration.
-
Distance Graph:
- Distance is the area under the velocity-time graph.
- Calculate the area of each segment (rectangle or triangle) under the velocity curve to sketch the distance graph. Each segment represents the distance traveled over time.
(b) Average Acceleration between and min
- Formula:
- Initial velocity km/h, final velocity km/h, min = h.
(c) Average Acceleration between and min
- Initial velocity km/h, final velocity km/h, min = h.
Would you like a detailed sketch of the acceleration and distance graphs? Let me know if you have any questions!
Related Questions:
- How would the graph of acceleration differ for a more gradual acceleration phase?
- How can the area under a velocity-time graph be used to find the exact distance traveled?
- How do you determine instantaneous acceleration from a velocity-time graph?
- What is the physical significance of negative acceleration on this graph?
- How would the velocity-time graph change if the car started decelerating from min instead of increasing speed?
Tip:
Always remember that the slope of a velocity-time graph represents acceleration, and the area under it represents distance traveled.
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Math Problem Analysis
Mathematical Concepts
Kinematics
Acceleration
Velocity-Time Graph
Formulas
Average acceleration: a_avg = (Δv / Δt)
Distance traveled: Area under the velocity-time graph
Theorems
Kinematic Equations
Suitable Grade Level
College Level (Physics 101 or 107L)
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