The graph shows the changes in the
distance walked by a dog in a time interval of eight seconds. At what time did the dog change its
The graph shown has distance on the
vertical axis and time on the horizontal axis. It consists of two straight-line
segments, one from zero to four seconds and another from four to eight seconds. So, the thing to recall here is
that a straight line on a distance–time graph indicates constant speed. So, we have two segments in which
the dog is moving with a constant speed, and the point where that changes is at a
time of four seconds. So, the time in which the dog
changed its speed was four seconds.
Next, we’re asked, “Was the dog
speed higher or lower before the point when its speed changed?”
To answer this, we need to remember
that speed is equal to the slope of a distance–time graph. The slope is higher in the first
segment than it is in the second one. And therefore, the speed before the
point when the speed changed was higher.
Finally, what is the difference
between the speed of the dog before and after it changed speed?
To answer this, we need to
calculate the slope of each of the two line segments. At the end of this first segment,
the dog had covered a distance of 12 meters, and that took four seconds. So, the speed in that segment is
three. And for the units, we take the
units of the vertical axis divided by the units of the horizontal axis. So that’s three meters per
second. By the end of the second segment,
the dog had covered 20 meters, but he started at 12 meters, so the distance is 20
minus 12. And the time is eight seconds at
the end of the segment minus four seconds at the start.
So, we have 20 minus 12, which is
eight, divided by eight minus four, which is four. So, the speed in the second segment
is eight divided by four, which is two. And again, that’s meters per
second. So, the difference between the
speed of the dog before and after it changed speed is three minus two equals one
meter per second.