Video Transcript
The diagram below shows the
velocity of two students, where 𝑑 equals two meters and 𝑡 equals 0.5 seconds. What is the difference between the
velocity of student 𝐴 and the velocity of student 𝐵? The answer should be given to one
decimal place.
Here, we are given a
displacement–time graph that shows the velocities of two students. This graph has displacement on the
vertical axis and time on the horizontal axis. We are asked to find the difference
between student 𝐴’s velocity and student 𝐵’s velocity when we are given the values
of the variables 𝑑 and 𝑡 that are used on the distance and time axes,
respectively. We’re told that 𝑑 is equal to two
meters and 𝑡 is equal to 0.5 seconds. We need to find the velocity of
each student, so let’s recall how velocity is defined.
The velocity of an object is equal
to its displacement divided by the time over which that displacement occurred. We can get the displacement and
time information for each of the two students from the graph that we’ve been given
and use this to calculate their respective velocities.
Let’s call the velocity of student
𝐴 𝑉 sub 𝐴 and the velocity of student 𝐵 𝑉 sub 𝐵. From the displacement–time graph,
we can see that student 𝐴 has undergone a displacement of three 𝑑 during a time of
𝑡. This means that 𝑉 sub 𝐴 is equal
to three 𝑑 divided by 𝑡. Similarly, we can see from the
graph that student 𝐵 has undergone a displacement of two 𝑑 in a time of three
𝑡. So 𝑉 sub 𝐵 is equal to two 𝑑
divided by three 𝑡.
We can now substitute in our values
for the variables 𝑑 and 𝑡 into these expressions for the velocities 𝑉 sub 𝐴 and
𝑉 sub 𝐵. For student 𝐴, we have 𝑉 sub 𝐴
equals three times two meters divided by 0.5 seconds. This works out as a velocity of 12
meters per second. Meanwhile, for student 𝐵, we have
𝑉 sub 𝐵 equals two times two meters divided by three times 0.5 seconds. This works out as a velocity of 2.6
recurring meters per second.
We are asked to work out the
difference in the velocities of student 𝐴 and student 𝐵. That means that we need to subtract
student 𝐵’s velocity, 𝑉 sub 𝐵, from student 𝐴’s velocity, 𝑉 sub 𝐴. 𝑉 sub 𝐴 minus 𝑉 sub 𝐵 is equal
to 12 meters per second minus 2.6 recurring meters per second. This difference works out as 9.3
recurring meters per second.
Note that the question asks for our
answer to one decimal place. Our answer then is that to one
decimal place, the difference between the velocity of student 𝐴 and student 𝐵 is
equal to 9.3 meters per second.
