### Video Transcript

A body was moving with a uniform
velocity of magnitude five centimeters per second from the point π΄ to the point πΆ
passing through the point π΅ without stopping. The distance between the body and
point π΅ is given by π of π‘ is equal to five multiplied by the absolute value of
eight minus π‘, where π‘ is the time in seconds and π is the distance in
centimeters. Determine the distance between the
body and the point π΅ after five seconds and after 11 seconds.

We are given a diagram which shows
the body that is about to move from point π΄ to point πΆ via point π΅ with a
velocity of five centimeters per second. Whilst there is a lot of
information in this question, the key point is that the function π of π‘ is equal
to five multiplied by eight minus π‘. π of π‘ is the distance of the
body from point π΅ after a given time. We need to calculate this distance
after five seconds and also after 11 seconds. After five seconds, π‘ is equal to
five. Therefore, we need to calculate π
of five.

This is equal to five multiplied by
the absolute value of eight minus five. Eight minus five is equal to three,
so we need to multiply five by the absolute value of three. As the absolute value of a number
is its distance from zero, the absolute value of three is three. As five multiplied by three is
equal to 15, the distance between the body and the point π΅ after five seconds is 15
centimeters.

We need to repeat this process when
π‘ equals 11. This means we need to calculate the
value of π of 11. This is equal to five multiplied by
the absolute value of eight minus 11. Eight minus 11 is equal to negative
three. As the absolute value of a number
is its distance from zero, the absolute value of negative three is also three. In fact, the absolute value of any
number will always be positive. Multiplying five by three once
again, we see that the distance between the body and point π΅ after 11 seconds is
also 15 centimeters.

In terms of our diagram, we can see
that after five seconds and 11 seconds, the body is the same distance away from
point π΅. After five seconds, it is still
approaching point π΅ from point π΄. And after 11 seconds, it is past
point π΅ and itβs heading towards Point πΆ.