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## Displacement, velocity, and time

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## Video udskrift

Let's do one more
example dealing with displacement,
velocity, and time. So we have if Marcia travels for
1 minute at 5 meters per second to the south, how much
will she be displaced? Let me do it this way. We know that velocity
is equal to displacement divided by time. And 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. Because this cancels out. You get displacement. And I'll flip this around. What's on the right-hand
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 us for displacement. They're asking us how much
did Marcia get displaced? And they're saying that
she travels for 1 minute. So this 1 minute right over
here, this is her time. Sometimes you could view
that as her change in time. Or it really is
her change in time. If it said 0 minutes on her
stopwatch when she started, at the end it'll say 1 minute. Or if it said 5
minutes, if maybe it was 3:05 when she
started, it would be 3:06 when she finished. So it was really
the change in time. Once again, I won't
write the delta there just because 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 1 minute, so the t
right over here is 1 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, look, 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 that when we're talking about
displacement, we're going to think about a magnitude
of how much it's 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 1 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 that you're going to get 5 and have
some weird thing here. So in order for it
to all work out, you have to either convert
the 5 meters per second to 5 meters per minute. Or let me phrase
that 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. And the minute is essentially
in the numerator right now. We could put this over 1. But it's essentially
in the numerator. So we want to divide by minutes. And we want to
multiply by seconds. We want seconds
in the numerator. And so how many seconds
are there per minute? You have 60 seconds
for every 1 minute. And so you have a minute
cancelling out with the minutes. And so now you have
5 meters per second to the south times 60 seconds. This is now cool because you
have seconds and seconds. I wrote "sec" there,
but this is also sec. So now you have
seconds over seconds. Those cancel out. And so your
displacement is going to be equal to 5 times 60. And then your units
left are meters. All the time units have
cancelled out and then it's meters to the south. So 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 could say that she
traveled 300 meters. Just that part. The magnitude of
the displacement, that is the distance
that she traveled.