Math Problem Statement

This distance-time graph shows the journey of a robin. Calculate the average speed of the robin between 4 and 14 seconds.

Solution

To solve this problem, we need to calculate the average speed of the robin between 4 and 14 seconds.

Step-by-Step Solution

  1. Identify the Distance at Specific Times:

    • From the graph:
      • At t=4t = 4 seconds, the distance is approximately 10 meters.
      • At t=14t = 14 seconds, the distance is approximately 30 meters.
  2. Calculate the Change in Distance (Δd\Delta d): Δd=30m10m=20m\Delta d = 30 \, \text{m} - 10 \, \text{m} = 20 \, \text{m}

  3. Calculate the Change in Time (Δt\Delta t): Δt=14s4s=10s\Delta t = 14 \, \text{s} - 4 \, \text{s} = 10 \, \text{s}

  4. Calculate the Average Speed (vv): v=ΔdΔt=20m10s=2m/sv = \frac{\Delta d}{\Delta t} = \frac{20 \, \text{m}}{10 \, \text{s}} = 2 \, \text{m/s}

Therefore, the average speed of the robin between 4 and 14 seconds is 2 meters per second (m/s).

Would you like further details on any step?

Here are some related questions that you might find useful:

  1. How can you find the speed at any specific moment from a distance-time graph?
  2. What does it mean if the graph has a steeper slope?
  3. How would you calculate the total distance traveled by the robin over the entire graph?
  4. What units are typically used for speed, and why?
  5. How does average speed differ from instantaneous speed?

Tip: When dealing with a distance-time graph, the slope of the line at any point gives the instantaneous speed, while the average speed can be calculated by looking at the overall change in distance and time.

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Math Problem Analysis

Mathematical Concepts

Average Speed
Distance-Time Graph
Linear Relationships

Formulas

Average Speed = Total Distance / Total Time

Theorems

Concept of Slope in Distance-Time Graphs

Suitable Grade Level

Grade 6-8