Video Transcript
The distance–time graph shows an
object moving at a uniform speed. What is the speed of the
object? (A) Nine meters per second, (B) 2.5
meters per second, (C) 21 meters per second, (D) 90 meters per second.
In this question, we are asked to
find the speed of the object shown in the distance–time graph.
To find the speed, we just have to
find the gradient of the graph. This is because the gradient of a
graph is the change in the 𝑦-axis over the change in the 𝑥-axis, which in the case
of this graph would be the change in distance over the change in time. And distance over time is just
speed. This can be written as 𝑉 equals
Δ𝑑 over Δ𝑡, where 𝑉 is the speed, Δ𝑑 is the change in distance, and Δ𝑡 is the
change in time. So, we calculate the speed of the
object by dividing the distance the object has traveled by the time it takes to move
that distance.
Looking at the distance axis, we
see that the units start at zero meters, then the first marking is at three meters,
the second at six, and so on. The distance increases by three
meters for each marking. We note this because the end of the
line doesn’t have a marking. It’s just one above 12. This means that the distance
traveled must be three meters more than 12, so 15 meters. This gives us the change in
distance.
Now let’s look at time. For the time axis, we see that the
units start at zero seconds, the first marking is at two seconds, the second at
four, and so on. The time increases by two seconds
for each marking. And the end of the line matches up
with the third marking, indicating that the change in time is six seconds. This means that each 15-meter
increase in distance corresponds to a six-second increase in time. Substituting these values into our
equation for speed, we see that the speed is equal to 15 meters per six seconds.
All of the possible answer choices
here are whole numbers or decimals, so let’s simplify our expression. 15 divided by six is equal to
2.5. The units of speed for this graph
are meters per second. This means that the speed of the
object given by this distance–time graph is 2.5 meters per second. The correct answer is option
(B).
