To analyze the motion of the ball, let's first calculate the speed and velocity.
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Speed: Speed is a scalar quantity that refers to how fast something is moving regardless of direction. It is calculated as the total distance traveled divided by the total time taken.
- The ball rolls 9 m north and then 9 m south, for a total distance of: \[ 9 , \text{m} + 9 , \text{m} = 18 , \text{m} \]
- The total time for this motion is: \[ 3 , \text{s} + 3 , \text{s} = 6 , \text{s} \]
- Therefore, the average speed of the ball is: \[ \text{Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{18 , \text{m}}{6 , \text{s}} = 3 , \text{m/s} \]
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Velocity: Velocity is a vector quantity that refers to the rate at which an object changes its position, including direction. It can be calculated as the total displacement divided by the total time taken.
- The initial displacement is 9 m north, and then it moves 9 m south, resulting in a total displacement of: \[ 9 , \text{m (north)} - 9 , \text{m (south)} = 0 , \text{m} \]
- The total time remains 6 s, so the average velocity is: \[ \text{Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{0 , \text{m}}{6 , \text{s}} = 0 , \text{m/s} \]
In conclusion, the final results are:
- Speed: \(3 , \text{m/s}\)
- Velocity: \(0 , \text{m/s}\)
Thus, the correct answer is: The speed was 3 m/s, and the velocity was 0 m/s.