### Video Transcript

A person is late for an appointment
at an office that is at the other end of a long, straight road to his home. He leaves his house and runs
towards his destination for a time of 45 seconds before realizing that he has to
return home to pick up some documents that he will need for his appointment. He runs back home at the same speed
he ran at before and spends 185 seconds looking for the documents, and then he runs
towards his appointment again. This time, he runs at 5.5 meters
per second for 260 seconds and then arrives at the office.

We’re then asked three different
questions. So let’s begin with the first
one. How much time passes between the
person first leaving his house and arriving at his appointment?

It might be helpful to begin by
visualizing what happens at each stage of this person’s journey. The journey begins with running for
45 seconds towards the office. The person then realizes that
they’ve forgotten something they need, so they go home at the same speed as they
traveled before. So that means that the time will
also be 45 seconds. They then spend 185 seconds looking
for these documents but not traveling anywhere. And then, finally, he runs towards
the office at 5.5 meters per second for 260 seconds.

We’re then asked for the time that
passes between first leaving and then arriving at the appointment. So that means that we just add up
the four time periods: 45 seconds, 45 seconds, 185 seconds, and 260 seconds. And when we work that out, we get
535 seconds. And that’s the answer for the first
part of this question.

The next question asks us, what is
the distance between the person’s house and his office?

In order to find the distance, we
can use this information on the last stage of the journey, when we’re given the
speed and the time taken. We can remember that distance is
equal to speed multiplied by time. So we can fill in the values
then. The speed is 5.5, and the time is
260. It is always worthwhile making sure
that we do have the same equivalent units. In each case, the time unit is
given in seconds, so we can simply multiply these values. When we work this out, we get a
value of 1430. And the units here will be the
distance units of meters. And that’s the second part of this
question answered.

The third part of this question
asks, what is the person’s average velocity between first leaving his house and
finally arriving at his office? Give your answer to two decimal
places.

We can recall the formula that
average velocity is equal to net displacement over total time. In this problem, the net
displacement will simply be the direct distance between the man’s home and the
office. We have already calculated this
distance in the second part of the question. It’s 1430. And the total time taken in the
whole journey was 535 seconds. This gives us 2.672 and so on. And when we round that to two
decimal places, we have a value of 2.67 meters per second. So if the positive direction is
from home towards the office, then the person’s average velocity can be given as
2.67 meters per second.

It’s worth noting that if we’d been
asked for the average speed instead, we would’ve needed to know the distances in the
first two parts of the journey along with the distance in the final part of the
journey. In this case, average speed would
have been calculated by the total distance divided by the total time. However, since average velocity
uses displacement, then we have the value of 2.67 meters per second.