Question

A ball rolls 9 m north in 3 s , then is kicked back and rolls 9 m south in 3 s . What is true about the values of the speed and velocity of the ball?(1 point) Responses The speed was 3 m/s , and the velocity was 0 m/s . The speed was 3 m/s , and the velocity was 0 m/s . - no response given The speed was 3 m/s , and the velocity was 3 m/s . The speed was 3 m/s , and the velocity was 3 m/s . - no response given The speed was 6 m/s , and the velocity was 0 m/s . The speed was 6 m/s , and the velocity was 0 m/s . - incorrect The speed was 0 m/s , and the velocity was 3 m/s .

Answer 1

To analyze the motion of the ball, let's break it down step by step.

1. **Speed Calculation**:
- During the first part of the motion, the ball rolls 9 m north in 3 seconds. The speed can be calculated using the formula:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{9 \text{ m}}{3 \text{ s}} = 3 \text{ m/s}
\]
- In the second part, the ball rolls 9 m south in 3 seconds. The speed remains the same:
\[
\text{Speed} = \frac{9 \text{ m}}{3 \text{ s}} = 3 \text{ m/s}
\]
- The average speed over the entire motion (the total distance traveled divided by the total time) would be:
\[
\text{Total Distance} = 9 \text{ m (north)} + 9 \text{ m (south)} = 18 \text{ m}
\]
\[
\text{Total Time} = 3 \text{ s} + 3 \text{ s} = 6 \text{ s}
\]
\[
\text{Average Speed} = \frac{18 \text{ m}}{6 \text{ s}} = 3 \text{ m/s}
\]
- Therefore, the speed is consistently 3 m/s.

2. **Velocity Calculation**:
- Velocity is a vector quantity, which means it has both magnitude and direction. When the ball moves north, its velocity is +3 m/s (assuming north is positive). When it moves south, its velocity is -3 m/s.
- The displacement is calculated as follows:
- Displacement from the starting point to the end point is 0 m (since it ends up back where it started).
- Given that:
\[
\text{Velocity} = \frac{\text{Displacement}}{\text{Total Time}} = \frac{0 \text{ m}}{6 \text{ s}} = 0 \text{ m/s}
\]

In conclusion:
- The speed of the ball is **3 m/s**.
- The velocity of the ball is **0 m/s**.

Therefore, the correct response is:
**The speed was 3 m/s, and the velocity was 0 m/s.**