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.