Video Transcript
Which of the following can be
determined from a distance–time graph? Is it (A) only the distance moved
by an object, (B) the distance moved by an object and the speed of the object, or
(C) only the speed of an object?
To think about this, let’s draw an
example of a distance–time graph. Suppose this plotted line
represents the motion of an object. We can see the distance that the
object has traveled and how long it has traveled for. This question is basically asking
us “What information can we learn about this object’s motion from a graph like
this? Is it only distance, distance and
speed, or only speed?”
Answer choice (C) suggests that a
distance–time graph can’t show the distance our object has moved. But we know this is false since the
vertical axis represents exactly that. Without showing distance, it
couldn’t be a distance–time graph. Let’s eliminate answer choice
(C).
To decide between the other two
answer choices, we should ask “Can the speed of an object also be determined by the
graph?” If so, then we know (B) is
correct. And if not, then (A) is
correct.
We can recall that speed is equal
to distance divided by time. Because of this, we can calculate
this object’s speed by dividing the line’s change along the vertical axis, which
represents distance, by the change along the horizontal axis, which represents
time. This corresponds to the slope or
gradient of the line. And as this line is straight or has
a constant slope, this means that the object moves at a constant speed.
The object moves three meters in
three seconds, so its speed must equal three meters divided by three seconds. Thus, it has a uniform speed of one
meter per second. So using a distance–time graph, we
were able to successfully determine the speed of an object. Because a distance–time graph can
give us information about both the distance moved by an object and the speed of an
object, the correct answer is (B).
