Video Transcript
A man walks in a straight line. His displacement from his starting
position is shown on the graph. How does his speed at a time four
seconds after he started walking compare to his speed at a time 12 seconds after he
started walking? (A) His speed after four seconds of
walking is slower than his speed after 12 seconds of walking. (B) His speed at a time four
seconds after he started walking was equal to his speed at a time 12 seconds after
he started walking. (C) His speed at a time four
seconds after he started walking was greater than his speed at a time 12 seconds
after he started walking.
In this question, we have a
displacement–time graph and we want to compare the speed of the man walking after
four seconds and after 12 seconds. We begin by noting that this is a
displacement–time graph and not a distance–time graph. We can recall that displacement is
a vector and distance is a scalar. So, to get the speed, we will need
to take the absolute value of the slopes on the displacement–time graph. So, let’s find the slope of the
line four seconds after the man starts walking.
The formula for the slope of a
straight line is given by the vertical difference over the horizontal
difference. The line is straight from time 𝑡
equals zero seconds to 𝑡 equals six seconds. So we can choose any two points
along this line, as long as they are on the same straight-line segment. For convenience, let’s choose the
start of the line at 𝑡 equals zero seconds and our endpoint at 𝑡 equals six
seconds.
At 𝑡 equals zero seconds, the
displacement is equal to zero meters. And at 𝑡 equals six seconds, the
displacement is equal to nine meters. So, the slope of the line at four
seconds is given by nine meters minus zero meters over six seconds minus zero
seconds, which equals 1.5 meters per second. And to find the speed, we need to
take the absolute value of this slope. Doing this, we find that the speed
of the man at a time four seconds after he started walking is equal to 1.5 meters
per second.
Now, let’s find the slope of the
line 12 seconds after the man starts walking. The line is straight from time 𝑡
equals 10 seconds to 𝑡 equals 16 seconds. So, let’s choose the start of the
line to be 𝑡 equals 10 seconds and our endpoint to be 𝑡 equals 16 seconds. At 𝑡 equals 10 seconds, the
displacement is equal to nine meters. And at 𝑡 equals 16 seconds, the
displacement is equal to zero meters. So, the slope of the line at 12
seconds is given by zero meters minus nine meters over 16 seconds minus 10 seconds,
which equals negative 1.5 meters per second.
And to find the speed, we need to
take the absolute value of this slope. Doing this, we find that the speed
of the man at a time 12 seconds after he started walking is equal to 1.5 meters per
second. We can now see that the speed of
the man at a time four seconds after he started walking is equal to his speed at a
time 12 seconds after he started walking.
This means that options (A) and (C)
are incorrect. So, option (B) must be the correct
answer, which is what we have calculated. His speed at a time four seconds
after he started walking was equal to his speed at a time 12 seconds after he
started walking.
