Video Transcript
A blue object and an orange object
move across a grid of equally spaced lines. Both objects move for four
seconds. The arrows show the distances moved
each second. Which color object has greater
average speed?
When we take a look at the motion
of these two objects on the grid, we know, first of all, that all the grid spaces
are of the same size. So, for example, this distance here
is the same as this distance here, and it’s also the same as this distance here, and
so on. For each object, the black arrows
show us how far that object moves every second. In the first second of time, the
orange object moves across one grid space, same with the blue object. Then, over the second time
interval, both objects once again move one grid space. However, over the third second, the
orange object once again moves one grid space, but the blue object moves one, two,
three grid squares. Over the last one-second interval,
both objects once again move across one grid space.
We want to know which object has
greater average speed. The average speed of an object 𝑣
is in general equal to the total change in distance traveled by that object divided
by the total change in time elapsed. For our orange and blue objects,
we’ll calculate their average speed in terms of a number of grid spaces over
time. Because we’re solving for average
speed, we won’t need to look at each individual one-second time interval. Instead, as our equation tells us,
we’ll look for the change in these variables of distance and time overall.
For our orange object then, what is
its total change in distance Δ𝑑? And what is its total change in
time Δ𝑡? This object we see moves four grid
spaces, and it does this in a total time of four seconds. This tells us the orange object has
an average speed of one space per second. When it comes to our blue object,
the total distance traveled here is one, two, three, four, five, six spaces. And this also all happens in a time
of four seconds. Therefore, the blue object has an
average speed of three-halves of one space per second. Since three-halves is greater than
one, our answer is that it’s the blue object that has the greater average speed.
