Let's work through another few senarios involving displacement, velocity and time or distance, rate and
time. So over here we have Ben is running at a constant velocity of 3m/s to the east, three meters
per second to the east and this is a review, this is a vector quanity they are giving us the magnitude
and the direction, if they just said three meters per second then that would just be speed, this is
the magnitude its 3m/s and it is to the east and they are giving us the direction so this is a vector
quantity that's why it's velocity instead of speed. How long will it take him to travel 720 meters? I
will do it both with the vector version and maybe they should say how long it will take it to travel 720 meters to the east.
Make sure that I make it clear that it is a vector quantity because displacement suppose to distance
We will do it both ways. If we think about just the scalar version of it we said already that rate or
speed is equal to the distance you travel over some time. Some time people will write a triangle or delta
there for change in time. That\'s explicitly ment when you just write over time like that. So rate or
speed is equal to distance divided by time, now if you know they're giving us in this problem, they're
giving us the rate, if we think about the scaler part of it they're giving us the rate, they're telling
us that is 3m/s they're also telling us the time, or sorry they're not telling us the time, they're
telling us the distance and they want us to figure out the time. So they tell us the distance 720 meters
and so we just have to figure out the time. So we have, if we just do the scalar version we're not dealing
with velocity and displacement, we're dealing with rate or speed and distance. So we have 3m/s=720 meters or
some change in time. So we can algebracially manipulate this, we muiltiply both sides by time right over
there. And then we could take this once step at a time, so 3m/s times time is equal to 720 meters. And
that makes sense at least units wise because time is going to be in seconds and it cancels out with the
seconds in the denominator so you will just get meters so that just makes sense there. So if you want
to solve for time you can divide both sides by 3m/s and then on the left side they cancel out on the
right hand side this is going to be equal to720 divided by 3 times meters then m/s of the denominator,
if you bring it out to the numerator you take the inverse of it so that's m, meters was on top, so 720
meters and now you're dividing by m/s and that's the same thing as multiplying by the inverse times s/m
and so what you're going to get here the meters are going to get 720 divided by three seconds so what
is that, 720 divided by 3, 72 divided by 3 is 24, so this is going to 240 this part riight over is going
to be 240. It's going to be 240 seconds, that's the only unit we're left with. On the left hand side
we just had the time, so the time is 240 seconds. Sometimes you'll see it and just to show you know in
some physics classes they show all these formulas, one thing i really want you to understand as we go
through this this journey together is that all those formulas are really algebraic minupulations of each other. You really
shouldn't memorize any of them you should always, hey that's just manipulating one of those other formulas
that i got before. One of those, even these formulas are only reasonably common sense. So you can start
from very common sense things rate as distance divided by time and then just manipulate it to get other
common sense things so we could've done it here. We could've multiplied both sides by time before we