Let's do one more example dealing with displacement, velocity and time. So we have: If Marcia travels

for 1 minute at 5 m/s to the south, how much will she be displaced? And so we know, we know that

that velocity (let me do it this way) we know that velocity is equal to displacement

is equal to displacement divided by time, it's really once again, it is change in time

but we'll just say time, that's implicitly change in time

and if you manipulate this a little bit

you really just multiply both sides by time

you just multiply both sides by the variable 't'

you get displacement, cuz this cancels out...

...you get displacement, and I'll flip this around

I'll write...what's on the righthand side I'll write on the left

so you get displacement is equal to time times velocity

or velocity times time

is equal to velocity times time or velocity times change in time

so over here they're asking for displacement

they're asking us how much did Marcia get displaced

and they're saying that she travels for one minute

so this one minute right over here, this is her time

sometimes you can do that as her change in time

it really is her change in time

whatever...you know...if it said 0 minutes on her stopwatch when she started

at the end it'll say 1 minute

or if it starts at 5 minutes, or maybe it was 3:05 when she started, it'll be 3:06 when she finish

it was really the change in time

once again, I won't write the delta there, just cuz

it keeps it...this is the way you most frequently see it

but I want to tell you that these are the same thing for the purpose of this problem

because sometimes you'll see the delta there

so the one minute, the 't' right over here is one minute...

...one minute...

...at 5 meters per second to the south

this right over here is the velocity

they give us the magnitude, which is 5 meters per second

or you could say that's the speed

and they also give us the direction, to the south

so this right over here

is 5 meters per second to the south

so we might just say, hey if we want displacement

that's just going to be equal to

5 meters per second to the south times 1 minute

the problem here is, when we talk about displacement

we're going to think about a magnitude of how much its moved

so it'll be a distance of some kind, and some direction

we have our direction here, but we don't want any other units there

and if we just multiply this over here

we have a minute over here, but we have seconds in the denominator

you can't just cancel out a minute and a second

so you can't just say you're going to get 5, and have some weird thing here

so in order for it to all work out

you either have to convert the 5 meters per second to meters per minute

or let me phrase it in another way

you have to convert the 5 meters per second to some amount of meters per minute

not 5 meters per minute, it's going to be different

or you convert the 1 minute to seconds

so at least in my mind it's easier to convert 1 minute to seconds

so let's do that

so this is the same thing

1 minute times...

and we want to get rid of the minute, the minute is essentially the numerator right now

we can put this over one

but it's essentially the numerator

so we want to divide by minutes

and we want to multiply by seconds

we want seconds in the numerator

and so what is...how many seconds are there per minute?

you have 60 seconds for every 1 minute

and so you have a minute canceling out with the minutes

and so now you have 5 meters per second to the south times 60 seconds

this is now cool, cuz you now have seconds and seconds

I wrote 'sec' there, but this is also 'sec'

so now you have seconds over seconds, those cancel out

so your displacement is going to be equal to 5 times 60

and then your units left are meters

all the time units have canceled out

and it's meters to the south

and this is equal to...5 times 60 is 300 meters to the south

and we are done, that's how much she has been displaced

if they just wanted the distance, you can say that she traveled 300 meters

just that part, the magnitude of the displacement...

...that is the distance that she traveled