5. Intervals of Increase and Decrease
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See solution.
The given graph shows the speed of a car over time.
There are several intervals in which the function representing speed is constant. Let's label them with (a), (b), (c), and (d).
We want to interpret what the constant intervals might represent. Let's first look at the interval (a). If the speed is constant and fairly high, it means that the car is driving with a constant velocity. The speed in interval (c) is the same, so the car is moving with the same constant velocity as in interval (a).
| Interval | Velocity |
|---|---|
| (a) | constant, high |
| (b) | |
| (c) | constant, high |
| (d) |
The car's speed in the interval (d) does not change, but it is lower than in intervals (a) and (c). Therefore, the velocity is also constant but moderate.
| Interval | Velocity |
|---|---|
| (a) | constant, high |
| (b) | |
| (c) | constant, high |
| (d) | constant, moderate |
The last interval we have not interpret yet is interval (b). The speed in this interval is equal to 0. This means that in that time, the car is not moving.
| Interval | Velocity |
|---|---|
| (a) | constant, high |
| (b) | zero, car does not move |
| (c) | constant, high |
| (d) | constant, moderate |