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.
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