Video Transcript
Which color line on the graph shows
the greatest speed?
This graph is a distance–time
graph. Distance, time, and speed are all
connected by a mathematical equation. If we take the distance that an
object travels and divide that by the time taken to travel that distance, then that
fraction equals the object’s speed. For a distance–time graph then, the
slope of a line on the graph is equal to the speed of a given object. The steeper the slope, the greater
the speed. Notice that the distance and time
axes on this graph are unscaled; that is, we don’t know the time or distance value
at any given point on the graph. Here though, we’re just looking for
which of our three lines shows the greatest speed, that is, the greatest compared to
the other two.
We can answer this question without
knowing specifically what that greatest speed is. As we said, since objects’ speed on
a distance–time graph is equal to the slope of a line, the steepest of these three
lines, red, blue, and green, corresponds to the greatest speed. All three of the lines begin at
zero at the origin, but it’s the green line that travels the greatest distance in
the least amount of time. Visually, this means it has the
steepest slope. And therefore, it shows the
greatest speed. On this unscaled distance–time
graph, the green line shows the highest speed. As a side note, because these three
lines are all straight, they represent objects each moving with a constant
speed.
