Video Transcript
A blue object and an orange object
move across a grid of equally spaced lines. Both objects move for five
seconds. The arrows show distances moved
each second. Which color object has the greater
average speed?
We see here these blue and orange
objects moving across a grid of squares. We’re not told how long each side
length of a square grid is, but we do know that this distance is the same as the
square is wide. We can assume then that all of the
sides of these grid squares have the same length. For these two objects, each arrow
shows how far that given object moved every second. So, for example, the orange object
over the first second moved this distance; then over the second second, this
distance; over the third second, this distance; and so on. Over the entire five-second
interval, we see the orange object covers one, two, three, four, five grid
squares. It does this by moving one grid
square for every second of time.
For the blue object on the other
hand, over the first second, it moves one grid square and then the same thing over
the second second. But over the third time interval,
we see it covers two grid squares. And then over the fourth and fifth
time intervals, it covers one-half of a grid square. Like the orange object, over five
seconds, the blue object covers one, two, three, four, five grid squares. This fact is important for
comparing the average speed of these two objects. In general, the average speed of an
object 𝑣 equals the change in distance that that object experiences divided by the
change in time over which the object was moving.
To compare the average speeds of
our two objects then, we’ll look at the total amount of distance each one moved
divided by the total amount of time each one was moving. For our orange object, we saw that
it moved five spaces in five seconds of time. The blue object too covered a total
distance of five spaces in five seconds. Even though the orange object did
this by moving at a constant speed while the blue object did it moving at a
nonconstant speed, the average speed for each one over the entire journey is the
same. For our answer then, we’ll say that
both objects have the same average speed. This is because, on average, each
one moves the same amount of distance over the same amount of time.
