Question Video: Determining Total Distance Traveled Following a Path that Changes Direction Physics • 9th Grade

What is the total distance covered by someone who walks along the lines shown in the diagram?

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Video Transcript

What is the total distance covered by someone who walks along the lines shown in the diagram?

Okay, so in this question, we can see that we’re presented with a diagram and that this diagram contains three different lines. We are asked to find the total distance covered by someone who walks along the lines in this diagram. So let’s begin by recalling our definition of distance. Distance is defined as the length of the path between two positions. So let’s imagine that our person in the question begins here. The question tells us that they walk along the lines, so we can draw out the path that they must follow. First, they walk along this six-meter line and get to here. Next, they walk along this eight-meter line reaching this point. And finally, they walk along this three-meter line, ending up here.

Now we are asked to find the total distance covered, and we know from our definition of distance that this must be given by the length of the path that we have drawn. And since the path consists of three straight lines, then the length of this path must equal the sum of the lengths of each of these lines. In other words, if we label the distance covered by the person 𝑑, then this distance, which is the total length of the path that we have drawn, must be given by the length of the line we’ve labeled one plus the length of the line labeled two plus the length of the line labeled three. Now the diagram gives us the lengths of each of these lines, so let’s substitute these values in.

We know that the length of line one is equal to six meters, the length of line two is equal to eight meters, and the length of line three is equal to three meters. And so we have that 𝑑 equals the sum six meters plus eight meters plus three meters. When we calculate this sum, we get a result of 17 meters. And so we have our answer to the question that the total distance covered by someone who walks along the lines shown in the diagram is given by 17 meters.

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