The graph shown displays the change in distance moved by an object that travels at a constant speed for a time of eight seconds. The distance axis of the graph has a resolution of four metres. Only the values of distance that are integer multiples of four are recorded in the table shown. What distance value should be entered in the table for a time value of two seconds?
If we look at the graph on the bottom right here, we can see that the distance traveled by the object has been marked with an X at every one second. But in the table we are only given three values, that is, a distance of zero at time equals zero, a distance of 20 metres at time equals four seconds, and a distance of 40 metres at time equals eight seconds. These correspond to the points where the Xs lie on top of horizontal grid lines, which make them very easy to read off, such as a distance of 20 metres here at time equals four seconds.
So how do we find the distance value at a time value of two seconds? We first find the time value of two seconds on our horizontal axis. And then moving up from there, we can find the X on our graph. We then move across from there to our vertical axis to find what the distance value is at this point. And we can see that it’s about halfway between eight and 12 metres. So it’s about 10. But the vertical axis doesn’t have enough resolution for us to see clearly what that value should be.
To be sure of what the value should be, it’s helpful to look at the other points on the graph and to notice that the question specifies the object is moving at a constant speed. That means that if we join all these points together, we’ll get a straight line. Since the speed is constant, we know that the distance covered between zero and two seconds has to be equal to the distance covered between two and four seconds. So the distance value at two seconds must be halfway between the distance at zero seconds and at four seconds. Therefore, the distance value at a time value of two seconds is 10 metres. So let’s add 10 to our table.
And this will help with the next question, which asks, “What distance value should be entered in the table for a time value of three seconds?” So we find a time of three seconds on our horizontal axis, move upwards to locate the point, and then across to the vertical axis to find the distance value. This one is even harder to read off. It’s in between 12 and 16 metres, but it’s closer to 16 than to 12. So it’s probably about 15. But we need to refer to the table values to be sure.
Since the object’s traveling at a constant speed, we know that the distance covered between two and three seconds has to be equal to the distance covered between three and four seconds. Therefore, the distance value at three seconds is halfway between that at two seconds and that at four seconds, which is 15 metres. So we can enter 15 into our table for a time value of three seconds.
Now, the final part of the question asks, “What distance value should be entered in the table for a time value of six seconds?” If we look up the time value of six seconds on our graph, we find that it’s somewhere around 30 metres on our vertical axis. To provide a precise distance value at a time of six seconds, we can notice that it should be halfway between the values of four seconds and eight seconds, as the distance traveled in these two intervals should be the same.
Alternatively, we could say that if the object has traveled 15 metres in three seconds, it should travel another 15 metres in the next three seconds. And either way, we’ll find that the distance value at a time of six seconds should be 30 metres. So 30 can go into our table under a time of six seconds.