Kai was 200 meters north of the library when he remembered he had to return some books to the library. It took him 200 seconds to do the round trip.

Question

Which best describes Kai’s roundtrip?

His speed was 1 m/s, and his velocity was 0.
His speed was 2 m/s, and his velocity was 0.
His speed was 1 m/s, and his velocity was 1 m/s north.
His speed was 2 m/s, and his velocity was 2 m/s south.

Answer 1

To analyze Kai’s round trip, we must differentiate between speed and velocity.

1. Distance: Kai traveled 200 meters to the library and then 200 meters back, totaling a distance of 400 meters.

2. Time: The total time taken for the round trip was 200 seconds.

3. Speed: Speed is defined as the total distance traveled divided by the total time taken. Therefore, Kai's speed is:

   \[ \text{Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{400 \text{ meters}}{200 \text{ seconds}} = 2 \text{ m/s} \]

4. Displacement: Displacement is the change in position. Since Kai started 200 meters north of the library and returned to the library, his displacement is:

   \[ \text{Displacement} = \text{Final Position} - \text{Initial Position} = 0 \text{ meters} \]

   (He ended up at the library, which we can consider as the 0 point.)

5. Velocity: Velocity is defined as the displacement divided by the time taken. Thus, Kai's velocity is:

   \[ \text{Velocity} = \frac{\text{Displacement}}{\text{Total Time}} = \frac{0 \text{ meters}}{200 \text{ seconds}} = 0 \text{ m/s} \]

Now, reviewing the options given:

1. His speed was 1 m/s, and his velocity was 0. (Incorrect - speed is 2 m/s)
2. His speed was 2 m/s, and his velocity was 0. (Correct - speed is 2 m/s, and velocity is 0)
3. His speed was 1 m/s, and his velocity was 1 m/s north. (Incorrect - speed is 2 m/s, and velocity is 0)
4. His speed was 2 m/s, and his velocity was 2 m/s south. (Incorrect - velocity is 0)

The best description of Kai’s round trip is:

His speed was 2 m/s, and his velocity was 0.