Video Transcript
A car is moving from point 𝐴 to
point 𝐷 as shown in the diagram below. The car moves from 𝐴 to 𝐵 in 100
seconds, then from 𝐵 to 𝐶 in 40 seconds, and then from 𝐶 to 𝐷 in 60 seconds. Calculate the magnitude of the
car’s average velocity.
Let’s begin by recalling that the
average velocity, 𝑣, of an object is given by the formula 𝑣 equals Δ𝑠 divided by
Δ𝑡, where the object has some displacement Δ𝑠 over a time interval Δ𝑡. It’s important to remember that the
displacement of the car, Δ𝑠, 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 𝐴 to point 𝐷, this does not correspond to its
displacement. Rather, its displacement is simply
along the straight line connecting points 𝐴 and 𝐷, 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 𝐴 to 𝐵 to 𝐶 then 𝐷,
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 car’s displacement, rather than the
total distance it traveled.
Now, the car’s paths along the
first and third leg of its overall journey are parallel. Thus, if we were to connect all
four points 𝐴 through 𝐷, we’d make a parallelogram. Because of this, we can take the
magnitude of the car’s displacement to be 0.8 kilometers. Therefore, we know that Δ𝑠 equals
0.8 kilometers. It’ll be a good idea to convert the
displacement value from kilometers to plain meters. That way, we’ll 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 Δ𝑠 equals 800
meters.
Next, to find Δ𝑡, the time
interval, we just need to add up the total time that it took for the car to get from
point 𝐴 to point 𝐷. The time taken during the first,
second, and third part of the car’s overall journey was 100 seconds, 40 seconds, and
60 seconds, respectively. So, adding them together, we find
that Δ𝑡 equals 200 seconds.
Now that we have values for Δ𝑠 and
Δ𝑡, let’s go ahead and substitute them in to the formula for velocity. We find that the car’s 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.
