Math Problem Statement

What's the answer for 3 D.

What's the answer for 3 D.

Solution

To answer 3d, we need to calculate the average speed for the entire journey.

Step-by-Step Solution:

  1. Formula for Average Speed: Average Speed=Total DistanceTotal Time\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}

  2. Total Distance: From part 3c, the total distance traveled is: Total Distance=1600+3200+3200=8000m.\text{Total Distance} = 1600 + 3200 + 3200 = 8000 \, \text{m}.

  3. Total Time: From the graph:

    • Total time is from t=0st = 0 \, \text{s} to t=160st = 160 \, \text{s}. Total Time=160s.\text{Total Time} = 160 \, \text{s}.
  4. Average Speed: Substitute the values: Average Speed=8000160=50m/s.\text{Average Speed} = \frac{8000}{160} = 50 \, \text{m/s}.

Final Answer:

The average speed for the journey is: 50m/s\boxed{50 \, \text{m/s}}

Let me know if you want further clarification or have any additional questions!


Expanding Questions:

  1. How is the concept of average speed different from instantaneous speed?
  2. Can you explain why the total distance includes multiple sections?
  3. Why is the distance during uniform motion a rectangle on a speed-time graph?
  4. How would the calculation change if there was a different acceleration?
  5. Can you calculate average velocity for this journey if there was a direction involved?

Tip:

Always remember, the area under a speed-time graph represents the total distance traveled!

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Math Problem Analysis

Mathematical Concepts

Average Speed
Distance-Time Relationship
Speed-Time Graphs

Formulas

Average Speed = Total Distance / Total Time
Area under Speed-Time Graph = Distance Traveled

Theorems

The area under the speed-time graph represents total distance.

Suitable Grade Level

Grades 9-10