Video Transcript
The graph shows the distance
Amelia traveled over her two-hour bike ride. Which of the following is
true? A) She traveled at a constant
speed of four miles per hour for the last hour. B) She traveled at a constant
speed of 10 miles per hour for the entire ride. C) She traveled at a constant
speed of eight miles per hour for the last hour. Or D) she traveled at a
constant speed of seven miles per hour for the entire ride.
We can see from the graph that
the 𝑥-axis represents the time in hours and the 𝑦-axis represents the distance
in miles. The speed or velocity in any
distance-time graph can be calculated by dividing the change in distance between
any two points by the change in time. If the graph is a straight line
for the entire journey, then they will be traveling at a constant speed. We can see from the graph that
three parts of the journey have different slopes or gradients. This means that, during these
three parts, Amelia will be traveling at different speeds.
We can therefore rule out
options B and D, as these stated that she traveled at a constant speed for the
entire ride. This is not the case as she
will have traveled at three different speeds. Both of the other statements
relate to the last hour of Amelia’s journey. This occurs between the two
points 𝐴 and 𝐵 on the graph. We can calculate the slope
between any two points on a graph by using the following formula, 𝑦 two minus
𝑦 one over 𝑥 two minus 𝑥 one. This is the change in
𝑦-coordinates over the change in 𝑥-coordinates, in this case the change in the
distance over the change in the time.
Point 𝐴 has coordinates one,
10 and point 𝐵 has coordinates two, 14. The 𝑦-coordinates or distances
here are 14 and 10. The corresponding
𝑥-coordinates are two and one. 14 minus 10 is equal to four
and two minus one is equal to one. This means that the slope of
the line between points 𝐴 and 𝐵 is four. We could also have worked this
out by drawing a right-angled triangle on the graph. We can see here that the
distance has risen from 10 to 14. And the time has gone from one
hour to two hours. Four divided by one is equal to
four. So once again, the slope equals
four.
As the slope in a distance-time
graph is equal to the speed, we can conclude that the speed in the last hour was
four miles per hour. This rules out option C and
therefore option A is correct. Amelia traveled at a constant
speed of four miles per hour for the last hour.