### Video Transcript

A car is moving from point ๐ด to
point ๐ท as shown in the diagram below. The car moves from ๐ด to ๐ต in 100
seconds, then from ๐ต to ๐ถ in 40 seconds, and then from ๐ถ to ๐ท in 60 seconds. Calculate the magnitude of the
carโs average velocity.

Letโs begin by recalling that the
average velocity, ๐ฃ, of an object is given by the formula ๐ฃ equals ฮ๐ divided by
ฮ๐ก, where the object has some displacement ฮ๐ over a time interval ฮ๐ก. Itโs important to remember that the
displacement of the car, ฮ๐ , is simply the straight-line distance from its starting
point to its ending point. So, although the car drove along
this entire path to get from point ๐ด to point ๐ท, this does not correspond to its
displacement. Rather, its displacement is simply
along the straight line connecting points ๐ด and ๐ท, shown here with a dashed
line.

Note that if we were to use the
total distance that the car traveled all the way from point ๐ด to ๐ต to ๐ถ then ๐ท,
we would be calculating its average speed rather than its average velocity. So in order to answer this question
correctly, we need to be careful to use the carโs displacement, rather than the
total distance it traveled.

Now, the carโs paths along the
first and third leg of its overall journey are parallel. Thus, if we were to connect all
four points ๐ด through ๐ท, weโd make a parallelogram. Because of this, we can take the
magnitude of the carโs displacement to be 0.8 kilometers. Therefore, we know that ฮ๐ equals
0.8 kilometers. Itโll be a good idea to convert the
displacement value from kilometers to plain meters. That way, weโll end up with a final
velocity value in meters per second. We know that a kilometer equals
1000 meters. So, 0.8 kilometers equals 800
meters. So, we know that ฮ๐ equals 800
meters.

Next, to find ฮ๐ก, the time
interval, we just need to add up the total time that it took for the car to get from
point ๐ด to point ๐ท. The time taken during the first,
second, and third part of the carโs overall journey was 100 seconds, 40 seconds, and
60 seconds, respectively. So, adding them together, we find
that ฮ๐ก equals 200 seconds.

Now that we have values for ฮ๐ and
ฮ๐ก, letโs go ahead and substitute them in to the formula for velocity. We find that the carโs average
velocity is equal to 800 meters divided by 200 seconds. Finally, evaluating this
expression, we get a result of four meters per second, and this is our final
answer. We have found that the average
velocity of the car is four meters per second.