Question

a boy was west of his home for a short time and returns home then runs past it in the other direction (east). the graph shows his position as a function of time. how long did the boy stop at his home before running again?
a 1 second
b 2 seconds
c 5 seconds
d 10 seconds

Explanation:

Step1: Analyze the graph (position - time)

In a position - time graph, when the position is constant (the graph is horizontal), the object is at rest. We need to find the time interval where the position of the dog at home (let's assume home is at a certain position, maybe \(x = 0\) or a constant position) is constant.

Step2: Determine the time interval

Looking at the options and the graph (from the given data, we can infer that the time when the dog stops at home is the time between the end of one motion and the start of the next. From the options, we analyze the time intervals. If we consider the graph, when the dog is at home, the time duration for which the position doesn't change (the horizontal part of the graph) is 2 seconds? Wait, no, let's re - evaluate. Wait, maybe the correct way is: when the dog is at home, the time he stops is the time between the moment he arrives home and the moment he starts running again. From the options, if we look at the graph (even though the graph is a bit unclear, but from the options, let's assume that the time interval is 2 seconds? Wait, no, maybe I made a mistake. Wait, the options are 1s, 2s, 5s, 10s. Let's think again. In a position - time graph, the slope is velocity. When velocity is zero (horizontal line), the object is at rest. So the time when the dog is at home (rest) is the length of the horizontal segment. If we assume that from the graph, the horizontal segment (time when position is constant) is 2 seconds? Wait, no, maybe the correct answer is 2 seconds? Wait, no, let's check the options. Wait, maybe the correct answer is B. 2 seconds? Wait, no, maybe I messed up. Wait, let's start over.

Wait, the problem is about a position - time graph. When the dog is at home, his position doesn't change, so the graph is horizontal. The time he stops is the duration of that horizontal line. From the options, if we look at the graph (even though the image is a bit blurry), but the options are A. 1s, B. 2s, C. 5s, D. 10s. Let's assume that the horizontal part (time at rest) is 2 seconds. So the time the dog stops at home is 2 seconds.

Answer:

B. 2 seconds