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Current time:0:00Total duration:10:36

- [Teacher] A cheetah is running somewhere and you would love to see it, but since you like physics so much, instead of showing you the clip, I give you its velocity-time graph. Oooo. So let's see if we can analyze this graph and visualize what our cheetah is doing. So, what's a velocity-time graph? It's a graph that tells us
the velocity of any object, like our cheetah, at every moment in time. I like to think of it as
watching a speedometer of a car. It is just like that. The speedometer tells us what
the speed of our vehicle is at every moments in time. The only difference is, here
it not only gives us the speed, not only tells us how fast it's going, but it also tells us in what
direction the object is moving. That's what velocity is,
it's speed plus direction. How does this graph give us direction? Well, if the graph is
positive, like right now, like you can see over
here above the time axis, then we can say the object is moving in one particular direction,
let's say, to the right. Or maybe upwards, as an example. And if the graph were to
come below the t-axis, then we would say the
velocity is negative. Meaning, it's in the opposite direction. It could mean to the left
or it could mean downwards. Anything. And so, the graph gives us both
the speed and the direction. That's why it's called
velocity-time graph. But let's not worry too
much about the direction, we'll only concentrate on the speed part. So, what does the graph say? Well, the graph is saying
that a time to equal to zero, our cheetah has zero speed. But then as the time ticks,
look at what's happening. It's speed is increasing.
Can you see that? One second, it's speed is
increased, it's speed increases. So, it's speed is continuously increasing and at the end of five
seconds, it has reached 20 meters per second. So, if we had a speedometer
attached to our cheetah, then it would look somewhat like this. At time to equal to zero,
when we just start our timer, it has zero speed but then
it quickly accelerates. It's speed increases and
at the end of five seconds, it reaches a speed of
20 meters per second. And we don't know what happens
after that because the graph ends over there. And now I'm guessing we
can pretty much visualize what our cheetah is doing. So, let's say here is our
one-of-a-kind, pink cheetah. We know that at time to equal
to zero, its speed is zero. So, if we attach this speedometer to it, then as time ticks, it gets
faster and faster and faster. At the end of five seconds,
it hits 20 meters per second. Now one important thing to think about is, that just like when you're
looking at the speedometer of a vehicle, it only tells
us how fast it's going. But it doesn't tell us
where that object is, or where that vehicle is, right? Similarly, the velocity-time
graph also tells us only the speed, how fast
it's going, and it tells us in what direction it is going. But it doesn't tell us
anything about its location. Its position. So, I have no idea where this
cheetah was to begin with. It could have been at zero, but it could have been at 100 meters. Or maybe it would have
been at minus 100 meters. There is no information
about its position, but only about its speed and direction. Okay, now that we know how
our cheetah is getting faster and faster, it means
it's accelerating, right? When our objects change their speed, whether they increase it or decrease it, we say that object is accelerating. So, can we calculate it's acceleration by looking at this graph? Well, let's see. How do we calculate
acceleration in general? We define acceleration a
as the change in velocity divided by time. Change in velocity is always calculated as the final velocity V
minus initial velocity u. So, this is the change in
velocity divided by time. So let's see if we can look at
our graph and calculate this. In fact, you know what,
see if you can try this one yourself first. Go ahead, pause the video
and see if you can do this, if you can calculate the acceleration by looking at the graph. All right, let's see. We know at t equal to
zero, its velocity is zero. Let's call it as our initial u. And we know at five
seconds, its velocity is 20. Let's call that as v, that's our final. And so, acceleration
becomes final velocity minus its meters per second, minus initial velocity, which is zero. They're over the time
taken for that change. The time taken was five seconds. And that number equals 20 divided by five, so its five seconds. 20 divided by five,
that's going to be four meters per second per second. Which we call four meters
per second squared. That is the acceleration of our cheetah. What does it mean? It means our cheetah is gaining a speed of four meters per second every second. Every second, it's increasing its speed by four meters per second. That's the acceleration of our cheetah. Okay, now let's say there's
a deer that is chasing this cheetah. Oooo, things are getting very interesting. And its velocity-time graph is over here. We see that even this
deer is accelerating. Now, can you figure out
what is the acceleration of this deer? Is it more than the
cheetah or less than that? Again, pause the video and
see if you can do this. Okay, let's see. Again, at time zero, our
deer's velocity is zero. We can call that as initial. And notice at the end of
two seconds, it reaches 20. So, we'll call that as final. So, the acceleration for
our deer is going to be V minus u by the same formula. 20 minus zero divided by two
seconds, because it reaches 20 in only two seconds. And so that would equal 20 divided by two. That is 10 meters per second per second, or 10 meters over second squared. Which means that the deer
has a way higher acceleration compared to the cheetah. It makes sense, right? The cheetah took five seconds
to increase its speed to 20 and our deer only took two
seconds to increase its speed. So, it has a higher acceleration
and in this crazy world, because our deer is chasing the cheetah, can we say that the deer
will quickly catch up to it? May not be because remember,
we don't know anything about their initial
locations, initial positions. It could be totally
possible that the cheetah is miles ahead of the deer to begin with. So, we can't comment on
how long it will take to catch up at all. And now the most important
thing we can see from the graph is that the deer which
has a higher acceleration, has a much steeper graph
compared to the cheetah. I mean, if you were to
think of these as mountains which you are climbing, then
notice climbing this mountain is much steeper, it's much harder than climbing this one, right? And so this means that
in a velocity-time graph, if the graph is steeper,
more acceleration. If the graph is less
steep, less acceleration. And that's why we like these graphs. Because just at a glace, by
looking at the steepness, we can figure out which
has more and which has less acceleration. And this also helps us
understand one more thing. Again, if you were to
say climb this mountain, then regardless of where you are, whether you are over here or here or here, the steepness remains
exactly the same, right? I mean, it's not any harder
to climb the mountain here compared to over here. Since the steepness remains
the same, and the steepness represents acceleration, we can also say that the acceleration of
that cheetah is a constant. Meaning the cheetah is gaining velocity, its velocity is changing, but its acceleration does
not change with time. It means, every second it will gain four meters per second of
velocity, constant acceleration. Similarly, even for the deer,
it's a constant acceleration. But on the other hand, if the
graph was not a straight line, but instead, say it looked like this, then it's not a constant acceleration. I mean, notice in the first two seconds, it gains a lot of velocity,
very high acceleration. The next two seconds,
it gains a little bit. The acceleration has decreased. And then after four seconds notice, it's not gaining anything. The velocity remains 20,
acceleration becomes zero. Even if you look from the
steepness point of view, can you see that
initially, it's very steep. So, high acceleration. Less steep, low acceleration
and then the acceleration becomes zero. The graph is flat, acceleration is zero. And so if you had a graph
that looks somewhat like this, the acceleration is not a constant. It is initially very high and
then acceleration decreases. But for a straight line,
it means the acceleration remains a constant. And to understand the
difference even more, let's bring back our speedometer. So, if you could look at the speedometer for this kind of motion,
we would see initially the stick moves very fast
because the pick up is very high and then it slows down. Okay, here it is. Notice, initially it was very
fast, later it slows down. And then it's almost a constant. But if we again look at the
speedometer for this kind of motion, well notice
the pick up is uniform. Can you see that? It's uniformly picking up. And it is for that reason,
this is also called uniformly accelerated motion. That means this velocity is changing, but its acceleration is a constant. And so what did we learn in this video? We learned how to analyze
the velocity-time graphs, we saw that the steeper the
graph, more is the acceleration and we also saw, it does not
tell us about the position of an object, it doesn't
tell us where the object is to begin with. It only tells us about how
fast things are moving.