Question

Determining Instantaneous and Average Speeds
A graph titled Position versus time for with horizontal axis time (seconds) and vertical axis position (meters). The line runs in 3 straight segments from 0 seconds 0 meters to 4 seconds 12 meters to 6 seconds 12 meters to 12 seconds 0 meters.
Use the graph to determine the instantaneous speed at 2 seconds.


m/s

What is the average speed over the entire trip?

Answer 1

To find the instantaneous speed at 2 seconds from the graph described, you need to analyze the slope of the position vs. time graph at that point.

From the description:

1. From 0 seconds to 4 seconds, the line goes from (0,0) to (4,12). This indicates a constant velocity during this period.
2. The slope (speed) can be calculated as follows:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{12\, \text{m} - 0\, \text{m}}{4\, \text{s} - 0\, \text{s}} = \frac{12\, \text{m}}{4\, \text{s}} = 3\, \text{m/s}
\]

At 2 seconds, the position is increasing linearly, so the instantaneous speed at 2 seconds is also **3 m/s**.

### Average Speed Over the Entire Trip

To find the average speed over the entire trip, you can use the formula:

\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}
\]

1. The total distance traveled is from 0 meters to 12 meters (and then back to 0 meters), which means:
- Distance from 0 to 12 meters = 12 meters
- Returning back from 12 meters to 0 meters = 12 meters
- Total distance = 12 m + 12 m = 24 m.

2. The total time for the entire trip is from 0 seconds to 12 seconds, which is 12 seconds.

Now, we can calculate the average speed:

\[
\text{Average speed} = \frac{24\, \text{meters}}{12\, \text{seconds}} = 2\, \text{m/s}
\]

So, the average speed over the entire trip is **2 m/s**.