Question

ben walks 500 meters from his house to the corner store. he then walks back toward his house but stops to talk to a neighbor when he is 200 meters from the corner store. if it takes ben 910 seconds from the time he leaves his house until he stops to talk to his neighbor, what is his average velocity? (round your answer to the nearest tenth of a meter per second.) bens average velocity is m/s. 0.2 0.3 -0.3 -0.2

Explanation:

Step1: Determine displacement

Displacement is the final position minus the initial position. Initial position (house) is 0. He goes 500 m to the store, then back 200 m from the store. So his position relative to the house is \(500 - 200 = 300\) m. Displacement \(d = 300 - 0 = 300\) m.

Step2: Use average velocity formula

Average velocity \(v_{avg}=\frac{\text{displacement}}{\text{time}}\). Time \(t = 910\) s. So \(v_{avg}=\frac{300}{910}\approx0.3\) m/s? Wait, no, wait. Wait, wait, maybe I messed up direction. Wait, velocity is a vector, so direction matters. Wait, initial position is 0 (house), he goes to store (500 m from house), then walks back 200 m from store, so distance from house is \(500 - 200 = 300\) m. So displacement is 300 m (from house to that point). Wait, but let's recalculate: \(\frac{300}{910}\approx0.329\), rounded to tenth is 0.3? Wait, no, wait, maybe I made a mistake. Wait, no, wait: wait, the problem says "average velocity". Wait, maybe I messed up the displacement. Wait, initial position: 0. Final position: he walked 500 m to store, then back 200 m towards house, so his position is \(500 - 200 = 300\) m from house. So displacement is 300 m. Time is 910 s. So \(v=\frac{300}{910}\approx0.3\) m/s? Wait, but let's check again. Wait, 300 divided by 910: 300 ÷ 910 ≈ 0.329, which is approximately 0.3 when rounded to the nearest tenth? Wait, no, 0.329 rounded to the nearest tenth is 0.3? Wait, 0.329: the first decimal is 3, second is 2, so yes, 0.3. Wait, but wait, maybe I had the displacement wrong. Wait, no, let's re-express:

Wait, another way: displacement is final position - initial position. Initial position (house) is 0. He moves to store (position 500 m), then moves back 200 m towards house, so his position is 500 - 200 = 300 m. So displacement is 300 - 0 = 300 m. Time is 910 s. So average velocity is 300 / 910 ≈ 0.329, which is 0.3 when rounded to the nearest tenth. Wait, but the options have 0.3 as a choice. Wait, but let me check again. Wait, maybe I made a mistake in displacement. Wait, no, maybe the problem is that velocity is a vector, so if we consider direction, but the options have positive and negative. Wait, wait, maybe I messed up the direction. Wait, if we take the direction from house to store as positive, then his final position is 300 m (positive direction), so velocity is positive. So 300 / 910 ≈ 0.3 m/s. So the answer is 0.3 m/s. Wait, but let's calculate 300 divided by 910: 300 ÷ 910 ≈ 0.329, which is approximately 0.3 when rounded to the nearest tenth. So the average velocity is approximately 0.3 m/s.

Answer:

0.3