Question

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. 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.

Explanation:

Step1: Calculate total distance for round trip

Kai is 200 meters north of the library. For a round trip, he goes 200 meters south to the library and then 200 meters north back? Wait, no, round trip here: he was 200m north, so to return to library (round trip? Wait, round trip would be going to library and coming back? Wait, no, the problem says "return some books to the library" so round trip: from his position (200m north of library) to library (200m south) and then back to his original position? Wait, no, maybe the round trip is going to the library and coming back? Wait, the problem says "he had to return some books to the library" so he goes from 200m north to library (200m south) and then maybe back? Wait, no, the problem says "round trip" so total distance: 200m (to library) + 200m (back to original position)? Wait, no, maybe the round trip is from his position to library and back? Wait, the problem says "Kai was 200 meters north of the library... return some books to the library... round trip". So round trip: he goes from 200m north to library (200m south) and then back to his original position (200m north)? Wait, no, that would be 400m total distance. Wait, maybe the round trip is just going to the library and coming back? Wait, no, the problem says "it took him 200 seconds to do the round trip". Let's re-read: "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." So round trip: from his position (200m north of library) to library (200m south) and then back to his original position (200m north)? So total distance is 200 + 200 = 400 meters. Wait, but maybe the round trip is just going to the library and coming back? Wait, no, if he is returning books to the library, the round trip would be going to the library (200m) and then coming back to his original position (200m), so total distance 400m. But let's check the options. Wait, maybe the round trip is from his position to library and back? Wait, no, maybe the problem means that the round trip is going to the library (200m) and then back? Wait, no, let's calculate speed: speed = total distance / total time. Velocity is displacement / total time. Displacement is final position - initial position. If he starts 200m north of library, goes to library (200m south, displacement -200m) and then back to original position (200m north, displacement +200m), so total displacement is 0 (since he ends up where he started). So total distance: 200m (to library) + 200m (back) = 400m. Total time: 200s. Then speed = 400m / 200s = 2m/s? But that's not matching the options. Wait, maybe the round trip is just going to the library and back? Wait, no, maybe the problem is that he was 200m north, so to return to library (round trip: going to library and coming back? No, returning books to library: he goes from 200m north to library (200m south), that's the trip to return books, but the round trip would be going to library and coming back to his original position. But maybe the problem has a typo, or maybe the round trip is just going to the library and back? Wait, no, let's check the options. The options have speed 1m/s or 2m/s. Let's recalculate. Wait, maybe the round trip is 200m (to library) + 200m (back) = 400m, time 200s, speed 400/200=2m/s. But displacement is 0 (since he starts and ends at the same place), so velocity is 0. But one of the options is "His speed was 2 m/s, and his velocity was 0." Wait, but let's check again. Wait, maybe the round trip is only going to the library and back? No, maybe the problem is that he was 200m north, so the round trip is going to the library (200m) and then back to his original position (200m), total distance 400m, time 200s, speed 2m/s, velocity 0. But another option: "His speed was 1 m/s, and his velocity was 0." Wait, maybe I misread the distance. Wait, maybe the round trip is 200m (to library) and then 200m back? No, 200+200=400. Wait, maybe the problem means that the round trip is 200m (from his position to library) and then 200m back? No, that's 400m. Wait, maybe the problem has a mistake, but let's check the options. Let's see:

Option 1: speed 1 m/s, velocity 0.

Option 2: speed 2 m/s, velocity 0.

Option 3: speed 1 m/s, velocity 1 m/s north.

Option 4: speed 2 m/s, velocity 2 m/s south.

Wait, let's recalculate. Maybe the round trip is 200m (to library) and then 200m back? No, that's 400m. Wait, maybe the problem is that he was 200m north, so the round trip is going to the library (200m) and then back to his original position (200m), total distance 400m, time 200s. Speed = 400/200 = 2 m/s. Displacement is 0 (starts and ends at same place), so velocity is 0. So the option "His speed was 2 m/s, and his velocity was 0" would be correct. But wait, maybe the problem considers the round trip as just going to the library and back, but maybe the distance is 200m (to library) and 200m back, total 400m. But let's check the time: 200 seconds. So speed is 400/200=2 m/s. Velocity is 0 because displacement is 0. So the correct option is "His speed was 2 m/s, and his velocity was 0." Wait, but let's check again. Wait, maybe the round trip is 200m (to library) and then 200m back, but maybe the problem has a mistake, and the total distance is 200m? No, round trip implies going and coming back. Wait, maybe the problem is that he was 200m north, so to return to library (round trip: going to library and coming back? No, returning books to library: he goes from 200m north to library (200m south), that's the trip, but the round trip would be going to library and coming back to his original position. So total distance 400m, time 200s. Speed 2m/s, velocity 0. So the correct option is the one with speed 2 m/s and velocity 0.

Step2: Analyze velocity

Velocity is displacement over time. Displacement is final position - initial position. Since Kai starts 200m north of the library and ends up back at his original position (after round trip), displacement is 0. So velocity = 0 / 200s = 0 m/s.

Step3: Analyze speed

Speed is total distance over time. Total distance for round trip: 200m (to library) + 200m (back) = 400m. Time is 200s. So speed = 400m / 200s = 2 m/s.

Answer:

His speed was 2 m/s, and his velocity was 0. (The option with this description)