From race cars to rocket ships, fast things
captivate our attention, and things have only gotten faster. The very first commercially
available car traveled at just 12 miles per hour. It's pretty much like a fast run. By the 1950s,
cars could move 150 miles per hour. Any guess as to what the fastest commercially available cars
go at now? 270. Pretty good. But just what do we mean by these numbers? How fast something is
moving? What exactly do we mean? We've been thinking all about motion in our physics class.
We've talked about how displacement and distance are slightly different, that displacement is
thinking about the distance as the crow flies, whereas distance is the total length
traveled. And we're going to use these ideas to understand really carefully just
what we mean by these big speeds. Let's learn! [Intro music] First, let's review our lesson objectives.
We'll define speed, then we'll define velocity. Remember that these sound similar, but one is
actually a vector. Do you remember which one? Then we'll calculate speed and velocity.
On a long car trip, this is the dream: the open highway, no traffic, making good
progress toward your destination. You look down, and your speedometer says 70 miles per hour.
You're moving fast. Other times, though, you run into this: traffic lights, or worst,
traffic. Now your speedometer reads zero. So, how fast did you go on this trip? Well, the
answer is complicated. It depends. Sometimes 70, sometimes zero. What about on average,
though? That's what we'll start with. Let's think about a long car trip and calculate
average speed. Let's say that you're going on a 300-mile trip through this beautiful landscape,
and at the end of the trip, you get out of your car, and it's been six hours. How fast did you go?
Well, we can calculate this with our average speed equation, where we just take the distance
we traveled and we divide it by time. So, in this case, we would take 300 miles and we would
divide by six hours. When we do that, we're going to get 50 miles per hour. Well, let's focus
in on each of those units. We have miles here because that was the units for our distance, and
we have hours here because that was the units for our time. The "per" word there in the middle just
tells me that every single hour I went 50 miles. So, my average speed, the speed on average
through all that trip, even though sometimes I was stopped, sometimes maybe I was going 70, sometimes
30, the average speed was 50 miles per hour. That's one way to think about speed, but that's not the only speed that we
went. Remember that open stretch of road? How do we think about our speed here? Well,
that's what we call our instantaneous speed. It's what our speedometer reads out. It's
this speed we're going at any given moment. So, instantaneous speed is
your speed at any given moment. Pretty straightforward. Now, when we're
calculating speed, we always use distance, like we just saw. So, when we're calculating
average speed, we'll use distance. However, if we want to calculate what we call velocity,
we're going to actually use displacement, and I think it'll become clear in
just a second why. Remember that velocity is a vector. That means it has a
direction. If we consider the white path, it has no one clear direction. First, it's going
south, then a little north, then a little east, then a little south. The direction's all over
the place. But if we just think about drawing a line from the start to the finish, that
teal arrow now has a pretty clear direction. We're going toward the east. So, our velocity uses
displacement, which now has a clear direction, even if our trip is meandering. How do we
calculate velocity? Well, the average velocity is just displacement over time. And then one little
note: it adds a direction. It adds a direction. Alright, let's go ahead and give these
ideas a try. Let's calculate velocity. Well, recall that velocity is just displacement divided
by time. So, what we're going to do then is we're going to go ahead and put displacement up top,
which is just 12 miles, and we're going to divide that by 24 minutes, which is our time. So, we
take 12 and we divide it by 24. When we do that, what we're going to get is 0.5. And then we
need to think about the units. What should the units be? Well, remember that the units for
displacement are miles, so we'll put miles there, and then the units for our time are
minutes. So, we'll put divided by minutes. So, that's the units that we have. Last thing we
need to consider is that velocity is a vector. So, to really be complete, we need to put a direction
here. And notice that our arrow is pointing there from west to east on our map. And so we're going
to add east on here below our velocity. So, that's a complete answer: 0.5 miles per minute to
the east. It has a direction and a size because it's a vector. OK, now let's calculate speed.
For speed, we're going to take our larger number there, the distance, which turns out to be 24,
and we're going to divide it by our time again, which is also 24. When we divide 24 by 24, we get
1.0. And our units are the same that we solve for velocity because our distance is in miles and our
time is a minute. So, we're going one mile per minute, which is exactly the same, actually, as
60 miles per hour because, of course, there's 60 minutes in a mile. So, that means that the speed
of this trip was one minute per mile. OK, let's try another example where we calculate speed and
velocity. Now it's your turn to give it a shot. Go ahead and pause the video and try to calculate
speed and velocity for this trip below. Don't forget, velocity is a vector. Alright, what did you get?
Let's start with speed. So, speed, recall, always has the distance up top, which in this
case is 118 miles, and the time on the bottom, which in this case is 2.5 hours. When we
divide 118 by 2.5, we're going to get 47. What are the units? Well, in this case, because
our distance is in miles and our time is in hours, we're going to get miles per hour, a pretty normal
unit for speed. Alright, let's give velocity a try. For velocity, now we're going to want to
switch from distance up top to displacement, and the displacement is just 94 miles. So, 94,
then divided by 2.5, gives us 38 miles per hour. But don't forget that velocity is a vector, and
that means it has a direction. For this trip, our arrow is pointing a little to the north and
to the east. So, it's going north and east. So, we call that direction northeast. Now we have
both a direction and a speed for a velocity, which is what we should have for a
vector. What have we learned? Well, we introduced speed, particularly average speed,
and we contrasted that with instantaneous speed. And then we introduced velocity. Lastly,
we calculated speed and velocity. [Outro music]
