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Hi guys, here we are again. I'm going to solve now exercise 13 from page 128. This is a graph. Usually these graphs are a bit difficult for you, but once you start understanding how to proceed, shouldn't be especially difficult.

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So, in this kind of exercises the first data we have is the graph itself. So, this is the data and is the one that we are going to use to take the information.

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Okay, well, there are two parts. One says that we have to say if the moving object is moving towards or away from its origin, and then for each section we have to calculate the average speed and draw the space-time graph.

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Okay, so, if it's moving away or towards the origin, when the x, imagine that we are at one point, we are going farther and farther, then the x is increasing.

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And in that case, where the x is increasing as 1 and 3, the object is moving away from its origin, okay?

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Number two, as the distance is constant, it's supposed to be stopped, okay?

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So, it's not moving away and it's not moving towards its origin.

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and in part four you see that the distance to the origin is decreasing so it's moving

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towards its origin so we could summarize this by writing moving away from the origin

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moving away are one and three one and three and moving towards the origin

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r is only the stage four okay and number two is stopped okay so that's the for the the answer to

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the first question and now the second we have to calculate the the average speed so to do that

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we are going to do to look at the different parts of the graph

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ok so I prefer not to lose the graph from from the viewpoint so I'm going to

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move down this first solution so let's see if it works

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yes it works we can do that with the board in the school but I prefer to be

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with you then being able to do all this okay well so we will start with the

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first part or the first section so section one it says we have to write the

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average speed and the average speed is the space traveled over the time taken

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and the space traveled is the final position, x final minus x initial, okay?

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So if you travel a distance, you write the final position minus the

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initial position, that's the distance that you have traveled. So for the first

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section, you know that the final position is 20 meters, so you write 20 meters and

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And the initial position is 0, 0 meters. And what is the time taken? The time taken, okay, this is the final time minus initial time for that section. In this case is 2 seconds minus 0 seconds in the origin.

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So, this is 20 over 2, which is 10 meters per second.

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Okay, that's the average speed of the first section.

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Now, for section 2, I'm going to write it here, okay, to have in the view this diagram.

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So, V2, what is the final position?

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It's 20.

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the initial 20 again and the time the final time is 4 and the initial time is

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2 seconds which is 0 meters per second and this result agreed with what we

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thought in the first part where we said that in section 2 the object is stopped

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okay now we go to section 3 section 3 we will follow the same procedure so in

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section 3 the final position is 40 meters you always in a graph you have to

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look at the units so it's 40 meters minus the initial position that is this

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point that is 20 meters the final time is 4 seconds and the initial time is 2

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seconds so this is 14 minus 20 20 meters 4 minus 2 2 seconds so this is 10 meters

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second okay and finally section 4 okay we have to move this down again you have

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room for section 4 okay so there you are now section 4 oh sorry for that and you

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have to choose the pen okay section 4 we have V4 and in this case we know that

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the final position is 0 meters and the initial position is 40 and the final

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time is 10 seconds and initial time is 6 seconds so we have minus 40 meters over

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for seconds and this gives a result of minus 10 meters per second so in this

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case the speed is negative it's negative because it's moving towards the region

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okay as we had seen before and now finally says that we should represent a

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graph okay with with the space traveled against the time taken so we are going

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to do just under the graph okay right so we travel here space you know that one

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thing is the position that's one thing okay this is 10 I'm going to draw just

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the representative points this is six we have four and two okay so as I was

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saying the space or the distance traveled is so at the end in this

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movement you are at the origin point because you are zero meters at the

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beginning and at the end so many that you are going to some place and coming

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back the displacement so the distance from the final point to the initial

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point is 0 but the distance traveled on the path is not 0 so in the first part

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we are going to reach 20 I'm going to do it in this way because it's going to be

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so 20 a smaller scale then in this space we don't move this place we travel other

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20 more so we get 40 and then other 40 so this is this is not going to be

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completely to scale because otherwise it's not going we I know I won't have

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space okay so in the first part we will from the origin to 20 we cover 20 meters

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okay in the second part as we are stopped we don't cover any extra space

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then we cover 40 but in the last part we continue to 80 because if we go to a

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distance of 40 going back the total distance traveled is 80 meters so at the

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end of the journey we have traveled 80 meters okay so I hope this clarified the

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the graph which at a first view is a bit difficult for you okay this is not asked in the in the

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wording but if we want to calculate the total average speed is the total distance traveled

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which is 80 meters over the total time taken which is which is 10 seconds and is 8 meters per second

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and now as I usually ask you does this result make sense well if in stages 1

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3 & 4 the rate speed is 10 meters per second maybe positive for negative but

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we are moving at a velocity of 10 and in second we are stopped the total

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average speed should be something between 0 and 10 and 8 is between those

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numbers so this result makes sense ok so that's all for now continue working on

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this and see you soon bye