Now let's take an example of how we would describe the motion of an apple
especially using this displacements and velocities.
So in this example you say, travel for 4 meters at 4 meters per second for 2 seconds.
And then you change your speed and go only 1 meter per second and you do that for 4 seconds.
The question will be what is your average velocity?
So first before I jump into this, I recommend you give it a shot.
Pause and see if you can find, using the definitions we just introduced
what the average velocity is of an object that moves in the way described in this problem.
So let's see what this looks like.
The first thing we wanna do is remember the definition that we just introduced for the average velocity,
which is that the velocity average is equal to the total displacement
the distance you've travelled over the time that it took you to travel that distance.
The time is not so bad in this case.
We see that we started with 2 seconds and then traveled for 4 more seconds.
So this is 4 plus 2 or 6 seconds.
The question is what is the displacement?
Is there a way we can find this displacement just knowing the velocity
and the times which we are traveling those velocities?
Well, this is something we know that the distance will start with this being 1 and this being 2.
The initial distance, distance 1, is 4 meters per second for 2 seconds.
So you just say distance is velocity times time.
So the velocity as we just saw is 4 meters per second.
The time during which you travel a velocity is 2 seconds.
Your units of seconds cancel nicely, and we got that 4 times 2 is 8 meters.
Which makes sense intuitively again because if you're travelling 4 meters per second
and you do so for 2 seconds, you've gone a distance of 8 meters.
We're gonna do the exact same thing for the second distance
and say that the second distance is, its velocity times the time which you travel at that velocity.
This new velocity is just 1 meter per second, and we do so for 4 seconds.
We're introducing notation here as well,
you see that I'm putting parentheses around numbers to indicate multiplication.
This is because I would like to avoid using things like this at times
unless we're using scientific notation,
and try to avoid using dots because often this can be misinterpreted as an x for position which will,
which we've seen. And these dots can be interpreted sometimes as decimal points.
So we're going to avoid those in the future as much as possible though not always.
The units of seconds cancel here and we get 4 meters.
So this is great. We have the initial distance and then the new distance that you travel.
So with these two distances the total displacement,
the total distance that you've traveled is 8 plus 4.
And so we can see the average velocity is 12 meters and it took you a time of 6 seconds.
So that the total velocity, average velocity, is 12 divide by 6 or 2 meters per second.
And this will be your answer for the average velocity over this time interval.