Question

etermining Velocity
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 velocity between 6 and 12 seconds.


m/s

What was the velocity over the entire trip?


m/s

Answer 1

To determine the velocity between 6 and 12 seconds using the provided graph information, we can analyze the position changes during this time interval.

From the data you provided:
- At 6 seconds, the position is 12 meters.
- At 12 seconds, the position is 0 meters.

To calculate the velocity \( v \) between these two points, we use the formula for velocity:

\[
v = \frac{\Delta x}{\Delta t}
\]

Where:
- \( \Delta x \) is the change in position (final position - initial position),
- \( \Delta t \) is the change in time (final time - initial time).

### Step 1: Calculate \( \Delta x \) and \( \Delta t \)
- \( \Delta x = 0 \, \text{meters} - 12 \, \text{meters} = -12 \, \text{meters} \)
- \( \Delta t = 12 \, \text{seconds} - 6 \, \text{seconds} = 6 \, \text{seconds} \)

### Step 2: Calculate the velocity
\[
v = \frac{-12 \, \text{meters}}{6 \, \text{seconds}} = -2 \, \text{m/s}
\]

Thus, the velocity between 6 and 12 seconds is **-2 m/s**.

### Overall Velocity
To find the overall velocity for the entire trip, we can calculate the total change in position over the total time taken.

### Total Change in Position
- Initial position at 0 seconds: 0 meters
- Final position at 12 seconds: 0 meters

So, the total change in position (\( \Delta x \)) for the trip is:
\[
\Delta x = 0 \, \text{meters} - 0 \, \text{meters} = 0 \, \text{meters}
\]

### Total Time
The total time (\( \Delta t \)) for the trip is:
\[
\Delta t = 12 \, \text{seconds} - 0 \, \text{seconds} = 12 \, \text{seconds}
\]

### Overall Velocity Calculation
Using the same velocity formula:
\[
v_{\text{overall}} = \frac{\Delta x}{\Delta t} = \frac{0 \, \text{meters}}{12 \, \text{seconds}} = 0 \, \text{m/s}
\]

Therefore, the overall velocity of the trip is **0 m/s**.