In this video I go further into the concept of determining the area under a curve by summing up rectangles. This time by illustrating that the distance traveled is the same as the area under a velocity vs time curve.
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Area Under a Curve Example - Distance Travelled
Example
Suppose the odometer on our car is broken and we want to estimate the distance driven over a 30-second interval.
Solution:
We take speedometer readings every five seconds and record them in the following table:
| Time (s) | Velocity (mi/h) |
|---|---|
| 0 | 17 |
| 5 | 21 |
| 10 | 24 |
| 15 | 29 |
| 20 | 32 |
| 25 | 31 |
| 30 | 28 |
Let's convert the velocity to ft/s.
| Time (s) | Velocity (ft/s) |
|---|---|
| 0 | 25 |
| 5 | 31 |
| 10 | 35 |
| 15 | 43 |
| 20 | 47 |
| 25 | 46 |
| 30 | 41 |