The graph shows the distance travelled over time by a car. Find the average velocity of the car for the first four hours and then over the next three hours.
So, in this question, what we’re trying to do is find the velocity of the car for the first four hours, and then over the next three hours. And to do that, what we’re gonna use is a triangle that’s gonna help us find our formula. And that is the speed-distance-time triangle. And this tells us, if we want to find the speed, or velocity, it’s equal to the displacement, or distance, over time.
And we know that from looking at the triangle. Because we can see if we want the speed, then we’ve got the distance and the time. And the distance is above the time, so it means speed is equal to distance divided by time. Similarly, if you wanted to find the distance, this would be equal to speed multiplied by time. That’s because they’re next to each other in the triangle.
So, we’re gonna start with the first four hours. So, the first thing we know for the first four hours is that the time is gonna be equal to four because it is the first four hours. And we take a look at the graph, we can see that the distance is equal to 50 kilometres. And that’s because if we look, there’s the zero point. And then we go up to point 𝐵. And at point 𝐵, which is that the last point in the first four hours, we can see that the difference between these two points is 50 kilometres. And I’ve shown that on the graph as well.
So therefore, we can see that the average velocity is gonna be equal to 50 divided by four because that’s our distance divided by our time. And that’s gonna be equal to 12.5 kilometres per hour. And that’s because we’ve got 50 divided by four. Well, what you do is you half it which gives you 25, half it again which gives us 12.5. And then, it’s kilometres per hour because we had our distance in kilometres and our time in hours.
Well, that’s the first part solved because we’ve found the average velocity for the first four hours. So, now what we’re gonna do is take a look at the next three hours. So, again, the easy part to know is the time because it says the next three hours. So therefore, the time’s gonna be equal to three.
But this time, to enable us to find the distance, what we’re gonna do is take 50 away from 300. That’s cause we can see at the point 𝐶, at the end of the three hours, it has travelled 300 kilometres. And we know that at the point 𝐵, at the end of the first four hours, our car had traveled 50 kilometres. So therefore, the distance travelled in the next three hours is 300 minus 50, which is equal to 250 kilometres.
So, this time, the average velocity is gonna be equal to the distance, which is 250, divided by three, which is the time, which will give us an average velocity of 83 and a third kilometres per hour. And we can work this out using the bus stop method. So, we can see how many threes go into 250.
Well, first of all, no threes go into two. So, then we can carry the two. Then, we need to see how many threes go into 25. So, this is going to be eight, remainder one, so we carry the one. So then, we see how many threes go into 10. Well, this is three, remainder one. So therefore, we can say that 250 divided by three is 83, and then the remainder one over three, so 83 and a third. So therefore, we’ve answered the second part of the question.
So, we can say that the average velocities for the car are 12.5 kilometres per hour for the first four hours and 83 and a third kilometres per hour for the last three hours.