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This speed/time graph shows an athlete running a complete race. How long was this race?

To determine how long the race was, we need to calculate the total distance covered by the athlete. The distance can be found by calculating the area under the speed-time graph.

### Analyzing the Graph:
1. **Segment 1** (from \( t = 0 \) to \( t = 4 \) seconds):
   - The graph forms a right triangle with a base of \( 4 \) seconds and a height of \( 10 \, \text{m/s} \).
   - Area = \(\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \, \text{s} \times 10 \, \text{m/s} = 20 \, \text{m}\).

2. **Segment 2** (from \( t = 4 \) to \( t = 8 \) seconds):
   - The graph forms a rectangle with a base of \( 4 \) seconds and a height of \( 10 \, \text{m/s} \).
   - Area = \(\text{base} \times \text{height} = 4 \, \text{s} \times 10 \, \text{m/s} = 40 \, \text{m}\).

3. **Segment 3** (from \( t = 8 \) to \( t = 12 \) seconds):
   - The graph forms a right triangle with a base of \( 4 \) seconds and a height of \( 10 \, \text{m/s} \).
   - Area = \(\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \, \text{s} \times 10 \, \text{m/s} = 20 \, \text{m}\).

### Total Distance:
- Total distance covered = \( 20 \, \text{m} + 40 \, \text{m} + 20 \, \text{m} = 80 \, \text{m}\).

So, **the length of the race is 80 meters**.

If you have any more questions or need further details, feel free to ask!

**Related Questions:**
1. What was the average speed of the athlete during the race?
2. How would the graph look if the athlete maintained a constant speed throughout the race?
3. What was the athlete’s acceleration during the first 4 seconds?
4. How much time did the athlete spend at the maximum speed?
5. What would the speed-time graph look like if the athlete decelerated to a stop at the end?

**Tip:** In speed-time graphs, the area under the curve represents the total distance traveled, while the slope indicates acceleration.

Discover how to calculate the length of a race using a speed-time graph. Analyze the graph segments and compute the total distance covered. Includes detailed calculations and explanations. Ideal for high school students studying physics or mathematics.

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