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Course: High school physics (TX TEKS) > Unit 1
Lesson 1: Motion variablesAcceleration
Acceleration is the rate of change of velocity (a = Δv/Δt). The unit for acceleration is m/s/s, or m/s^2. Acceleration is a vector with magnitude and direction. If velocity and acceleration point the same direction, the object is speeding up. If velocity and acceleration point opposite directions, the object is slowing down. Changing direction is also a form of acceleration. Created by Mahesh Shenoy.
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Video transcript
- [Instructor] I decide to
race my regular household car with a sports car, say Ferrari. Well, clearly it's no match for me. It has a very high top speed, but what if we both agree,
for the sake of this race, to limit our top speed
to, say, 80 miles an hour? Now, do you think I have
a fair shot of winning? Well, let's find out. Three, two, one. (chuckling) Oh, no. Oh, no, why did that happen? (chuckling) We have the same top speed, right? Well, let's look at the speedometer and see if that gives us a clue. So let's try that again. Ooh, ooh, do you see what happened? Well, even though we both
have the same top speed, you can see the sports
car was able to pick up that speed much more quickly than my car. This idea of how quickly you can speed up or how quickly you can pick up speed is the idea of acceleration, and so although we both
have the same top speed, Ferrari or any sports car for that matter has a much higher, has a much higher acceleration
than regular cars, and that's why it was
able to extend that lead. So how do we define acceleration? Well, in physics in general,
acceleration is defined as the rate of change in velocity. In other words, it's a measure of how quickly your velocity is changing, and we'll take a lot of
examples to make this clear, but mathematically, this
means acceleration equals the change in velocity. The delta represents the
change in V as the volocity, change in velocity divided by
the time taken for the change, and so this will then equal how do you calculate
the change in velocity? Well, change in any quantity
is usually calculated as the final value minus the initial value divided by the time taken for that change. Now in the case of Ferrari, let's say it took about two seconds to reach the 80 miles an hour,
and my car took a lot of, I don't know, maybe it
took about 10 seconds or maybe even more, but
let's say 10 seconds. So let's calculate quickly what
will be their acceleration. So the acceleration of the Ferrari would be the final
velocity of the Ferrari, that is 80 miles an hour, minus
the initial start from zero, divide by two seconds. That gives us 40 miles
per hour per second, and similarly, what would be
the acceleration of my car? I'm just gonna call it as M for my car. Well, even here, the change
of velocity is the same. It goes from zero to 80, but it takes about 10 seconds to do that, and so that gives us about
eight miles per hour per second. So look, even though both
cars have the same change in velocity, Ferrari's able to change that velocity much more quickly, giving it a higher acceleration, and that's what this number says. It says per second, Ferrari picks up about 40
miles per hour velocity, whereas my car per second only picks about eight miles per hour velocity. So now let's see why acceleration
was so tricky for me. First and foremost, miles an
hour is not the standard unit. The standard unit is meters per second. So if I convert this 40 miles per hour, it turns out to be about
18 meters per second. Don't worry about the
conversion in this video. We'll tackle that separately, but that means the acceleration
in the standard terms becomes 18 meters per second per second. Again, what does it say? Now it's saying that every
second my Ferrari is picking up a velocity of 18 meters per second, and so if you simplify the unit, it then becomes meters per second squared, and that's not very intuitive, right? What is meters per second squared? Should always remember it is
meters per second per second, and the same is the case over here. Eight miles an hour, if I
convert it to meters per second, it gives me about 3.6 meters per second. So that is 3.6. Its velocity increases by 3.6
meters per second per second, or again, I can say it is 3.6
meters per second squared. So need to be mindful about the unit. It's meters per second squared, but here's another reason
why it was so tricky for me. My brain is to keep saying, "Acceleration is the
same thing as velocity." It's not. Acceleration is how quickly
the velocity is changing. It only exists when velocity changes. One way to check for it is by
looking at the speedometer, but if you don't have a speedometer, then we can look at the motion diagram. For example, if I take the snapshot of our Ferrari every half a second, let's look at what it looks like. What do we see? We see that in the first half second, it traveled a little bit of distance. In the next half second, it
traveled a little bit more. Then it traveled even more and so on. This tells me, aha, the
Ferrari must be accelerating because it's traveling
more and more distance in every subsequent time interval. Therefore, its velocity
must be increasing. It is accelerating, and this, by the way, is
called an oil drop diagram (chuckling) because if you imagine that your car was dropping oil, leaking oil every half
a second in this case, then you would get the
oil drops on the road looking something like this, and that brings me to another
point about acceleration. Look, velocity is a vector quantity. It has a direction, right, which means acceleration
is also a vector quantity. It, too, has a direction, and
again, my brain would say, "Hey, acceleration must
be the same direction in which the car is moving," but that's not always the case. Here's how to think about the direction. If the acceleration value
turns out to be positive, like in our example, then it has the same
direction as the velocity. So in our example, the
velocity is upwards, and since the acceleration
has a positive value, that means, in our example, acceleration must also
be upwards or forward, whatever you wanna call that. Let's see if we got this. Here's another oil drop diagram, and imagine the car is
again going forward. Can you pause the video and think about whether this car is accelerating, and if it is, what is the
direction of the acceleration? Pause and try. Okay, let's see. Here, I see that the distance between subsequent time
intervals is decreasing. So in this example,
velocity is decreasing. So it is still changing. Therefore, this car is also accelerating. Well, you might say, if it's slowing down, isn't it deceleration? You're right, but in physics, acceleration is a much more general word. Whether you are speeding
up or slowing down, the general term is acceleration. As long as the velocity is changing, we will say it's accelerating. So yes, this acceleration
is indeed a deceleration. Now what's the direction of this? Well, for that, I will look at
the sign of my acceleration. This time, since the final
velocity will be smaller than the initial velocity,
you'll see this will be negative. So here, the acceleration
would be negative, and negative acceleration means it is in the opposite
direction of the velocity. So since the velocity over here
is in the forward direction, in this case, acceleration
must be backwards. So look. Right in front of your eyes, you can see that acceleration
velocity need not be in the same direction. So look. In general, if your object is speeding up, if its velocity is increasing, acceleration and velocity
are the same direction. They would have the same sign. If one is positive, velocity is positive. Acceleration is also positive, but if your object is slowing
down, if it's decelerating, that's when acceleration would be in the opposite direction of the velocity. They would have opposite signs. If velocity is positive,
acceleration becomes negative. and again, let's just confirm
that with an animation. There you go, deceleration. Makes sense, right? Let's take a couple of more examples because you can never take too many examples with acceleration. So here's another oil drop diagram. Let's say the distance listed between the oil drops
are exactly the same. Velocity is upwards. What is the direction of the acceleration? Again, pause and try. Well, if the distance between the oil drop is exactly the same, that means this velocity is not changing. Its velocity is a constant. So there is no acceleration,
which means in this example, acceleration is zero constant velocity. So you see, this object could be moving at an extremely high velocity,
but that doesn't matter. It's not changing, and therefore,
there is no acceleration. Okay, what if our car is just stationary, sitting over there? What would be its acceleration? Well, this time, we don't
need an oil drop diagram. We can just imagine this. The velocity would be zero, but more importantly,
that velocity stays zero. It's not changing. In that case, also, the
acceleration would be zero. Here's a final oil drop diagram. This time, we have, again,
the oil drops are equidistant, same distance between the oil drops, but it's going in a curve. The car is going in a curve. What do you say about the acceleration? All right, if the distance
between them is the same, then I know that the
speed must be the same. So the acceleration must be zero, right? Well, we have to be careful. The speed is the same, but
velocity involves direction, and clearly, you can see that the direction is
continuously changing, which means, even though
the speed is the same, velocity is changing, and therefore, there must be an
acceleration in this case. So this car, even though it's
going at a constant speed, is accelerating because
the velocity is changing. I know it's tricky, but
it's always about the change in velocity, not change in speed. and now if you're wondering
what is the direction of this acceleration,
don't worry about it. We'll tackle direct accelerations in curved motions separately, but anyways, to sum it all
up, acceleration is a measure of how quickly your velocity, not speed, your velocity changes. It's measured as change in velocity divided by the time taken for
that change, and therefore, its units become this weird
meters per second square, but what does it mean? It's basically telling you how many meters per
second change in velocity is happening per second, and when things are
moving in straight line, if you're speeding up, if
your velocity is increasing, acceleration and velocity
in the same direction. If the velocity is decreasing,
if you're decelerating, if you're slowing down, then they will be in
the opposite direction, and of course, if the
velocity is not changing, your acceleration would be zero.