Video Transcript
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 we’re told shows the movement of an object that changes
from moving at one uniform speed to moving at a different uniform speed. We are asked to look at this graph
and figure out which of the colored lines represents the movement that has the
greater speed. In order to figure this out, we
will need to recall how to read a distance–time graph and how to use such a graph to
find an object’s speed.
A distance–time graph, like its
name suggests, is a graph measuring the distance that an object has traveled and the
amount of time that it has traveled for. We can see that we have distance
plotted on the vertical axis and time on the horizontal axis. Recall that the speed of an object
is defined as the distance traveled by that object divided by the time it traveled
for. This means we could find the speed
of each of this object’s movements if we had the values for this graph. But even without numerical values,
we can still compare the two line sections representing the two sections of
movement. In particular, we are interested in
the slope of the lines.
The slope of a line is defined as
the change in the vertical coordinate divided by the change in the horizontal
coordinate. Because the speed of an object is
equal to the distance traveled divided by the time taken and because the vertical
coordinate on a distance–time graph is distance and the horizontal coordinate is
time, then the slope of a line on a distance–time graph gives us the speed of the
object. A larger change in distance over a
given change of time will correspond to a steeper slope and a greater speed.
So let’s look at the blue and red
lines on this graph and compare them. Looking at the slopes of the lines,
we can see that the red line is steeper than the blue line. This means that the red line
represents the movement with the greater speed. Therefore, option (B), the red
line, is the correct answer.
