In this time interval, how far did the runner go each seconds

To find out how far the runner traveled each second during the last 2 seconds (from \( t = 2 \) to \( t = 4 \) seconds), we can examine the slope of the graph over this interval.

1. **Determine the total distance covered in the 2-second interval**:
   - From the previous analysis, the runner covered 30 yards from \( t = 2 \) seconds to \( t = 4 \) seconds.

2. **Calculate the distance covered per second**:
   - This interval is 2 seconds long, and the total distance covered is 30 yards.
   - Distance covered per second = \(\frac{30 \text{ yards}}{2 \text{ seconds}} = 15 \text{ yards/second}\).

So, the runner traveled **15 yards per second** during this 2-second interval.

Would you like more details or have any questions?

Here are some related questions for further exploration:
1. How does the runner's speed compare between the first 2 seconds and the last 2 seconds?
2. If the runner continued at the same speed, how far would they travel in the next 2 seconds?
3. How would you represent the runner's speed as a function of time?
4. What changes in the graph would indicate that the runner is accelerating?
5. How would you calculate the total distance traveled if the runner's speed varied during each second?

**Tip:** The slope of a distance-time graph represents speed. A steeper slope indicates a higher speed.

Explore how to calculate the distance a runner traveled per second using time interval analysis. This problem involves interpreting distance-time graphs and calculating average speed over specific intervals. Suitable for students in Grades 7-9.

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