Video Transcript
According to the figure, a body
moved from 𝐴 to 𝐵 along the line segment 𝐴𝐵, and then it moved to 𝐶 along
𝐵𝐶. Finally, it moved to 𝐷 along 𝐶𝐷
and stopped there. Find the distance covered by the
body 𝑑 one and the magnitude of its displacement 𝑑 two.
Looking at the figure, we’re told
that a body begins at point 𝐴, right here, and then follows the line segment 𝐴𝐵
to point 𝐵 then moves to point 𝐶 following this path, finally moving along line
segment 𝐶𝐷 to end up at point 𝐷. Given this motion, we want to
calculate the distance the body has covered, we call that 𝑑 one, and the magnitude
of its displacement 𝑑 two.
Clearing some space, let’s first
work on solving for the distance our body travels 𝑑 one. We can recall that distance in
general is equal to the total path length followed by some body as it moves from one
location to another. In our case, our body moved from
point 𝐴 to point 𝐷 along the path shown in orange. We see that that involves 6.6
centimeters of travel from point 𝐴 to point 𝐵, 8.8 centimeters from 𝐵 to 𝐸, 16.4
centimeters from 𝐸 to 𝐶, and on the last leg of the journey 12.3 centimeters. 𝑑 one then equals the sum of these
four distances. Adding them all up gives a result
of 44.1 centimeters. This is the distance our body
traveled.
And now let’s consider its
displacement magnitude 𝑑 two. Displacement is different from
distance in that displacement only takes into account the start point and end point
for some body. In our situation, our body begins
at point 𝐴 and it ends up at point 𝐷. So this straight pink line
connecting these two points represents the displacement magnitude 𝑑 two. We see that the length of this line
segment can be divided up into two parts: one part right here and then the second
part here. Each of these is a hypotenuse of a
right triangle. This means we can use the
Pythagorean theorem to solve for these lengths.
If we call the length of the first
hypotenuse 𝑙 one and that of the second 𝑙 two, then we can say that the
displacement magnitude 𝑑 two is equal to their sum and that 𝑙 one and 𝑙 two are
defined this way. 𝑙 one equals the square root of
6.6 centimeters quantity squared plus 8.8 centimeters quantity squared. And 𝑙 two equals the square root
of 16.4 centimeters quantity squared plus 12.3 centimeters quantity squared. When we enter these expressions on
our calculator, we find that 𝑙 one is equal to exactly 11 centimeters, while 𝑙 two
is 20.5 centimeters. Adding these together gives us a
result of 31.5 centimeters. This is the displacement magnitude
of our body.
