Video: Using the Equation of Motion in a Straight Line to Find the Magnitude of the Average Velocity

A person drove a car for 723 m on a straight road with a velocity of 9 km/h. He then continued for the same distance in the same direction, but with a velocity of 6 km/h. Find the magnitude of the average velocity during the whole trip.

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Video Transcript

A person drove a car for 723 metres on a straight road with a velocity of nine kilometres per hour. He then continued for the same distance in the same direction but with a velocity of six kilometres per hour. Find the magnitude of the average velocity during the whole trip.

So, to solve this problem, what we can think about is the speed–distance–time triangle or, in this case, the velocity–displacement–time triangle. And that’s because what we need to do in this question is find the average velocity during the whole trip. So therefore, if we look at velocity in our triangle, well we can see that velocity is gonna be equal to the displacement or distance divided by the time.

So therefore, to work out the average velocity for the whole trip, what I’m gonna need to do is the total distance of the whole trip and the total time for the whole trip. So, the total distance is gonna be equal to 723 multiplied by two. And that’s because we’re told that the person drove a car for 723 metres on a straight road with a velocity of nine kilometres per hour.

But then, we’re told that he continued for the same distance in the same direction but with a different velocity of six kilometres per hour. So, the total distance is gonna be 723 multiplied by two. And when we do this, we get 1446 metres. So, that’s the total distance for the whole trip.

Now, to work at the time for the whole trip, it’s slightly more complicated cause we need to find out the value of this cause we’re not told in the question. Well, the time is equal to the distance divided by the velocity. So therefore, we can work this out. We can work out the time for both sections of the journey.

So, when we do this, we’re gonna get time is equal to 0.723 divided by nine. We’ve got 0.723 because our distance is in metres. However, our velocity is in kilometres per hour. So therefore, we convert metres to kilometres. So, 723 metres is 0.723 kilometres. And then, this is plus 0.723 divided by six, which gives us an answer of 0.200 continued hours. So now, we’ve got the total distance for the whole journey. And we’ve got the total time for the whole journey.

So, now what we can do is calculate the average velocity. We can do this by dividing as we said in the beginning, the total distance by the total time, remembering that we need to turn the total distance into kilometres not metres. So, it’s gonna be 1.446 kilometres. So, the average velocity is gonna be equal to 1.446 divided by 0.200 continued. Which will give us an answer of 7.2 kilometres per hour, and I’ve rounded that to one decimal place.

So therefore, we can say that if is a person drove a car for 723 metres on a straight road with a velocity of nine kilometres per hour. Then, he continued for the same distance in the same direction but with a velocity of six kilometres per hour. The magnitude of the average velocity during the whole entire trip would be 7.2 kilometres per hour.

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