The distance–time graph shows an
object that changes from moving at one uniform speed to moving at a different
uniform speed. Which color line shows the greater
speed? (A) The blue line, (B) the red
line, (C) both lines show the same speed.
In this question, we are given a
distance–time graph that shows the movement of an object. The object changes speed from one
uniform speed to another. This is represented with a blue
line for the first uniform speed and a red line for the second uniform speed that
the object has. We are asked to look at this graph
and figure out which of the lines represents the movement with the greater
Before we begin to figure this out,
let’s remind ourselves how to read distance–time graphs and how to use them to find
the speed of an object. A distance–time graph plots
distance on the vertical axis against time on the horizontal axis. Let’s recall that the slope of a
line is equal to the change along the vertical axis divided by the change along the
horizontal axis. This means that the slopes of these
lines on the distance–time graph are equal to the change in the distance traveled
divided by the change in time, that is, the time taken to travel the distance.
Now, the question is asking us to
figure out which line has the greater speed, so let’s define what speed is. The speed of an object is equal to
the distance the object travels divided by the time taken to travel the
distance. Notice that this is the same
fraction that gives us the slope of a line on a distance–time graph. This means that the slope of a line
on a distance–time graph is equal to the speed of the movement represented by the
line. The steeper the slope of the line,
the greater the speed.
So, in order to find which line
represents the greater speed, we need to look at the blue line and the red line and
see which one has the steeper slope. Looking at the two lines, we can
see that the blue line has a steeper slope than the red line. This means that the blue line
represents the movement with greater speed. So option (A), the blue line, is
the correct answer.