Average Velocity for Constant Acceleration

Physics

Kinematic formulas and projectile motion

Average Velocity for Constant Acceleration
Acceleration of Aircraft Carrier Takeoff
Deriving Displacement as a Function of Time, Acceleration and Initial Velocity
Plotting Projectile Displacement, Acceleration, and Velocity
Projectile Height Given Time
Deriving Max Projectile Displacement Given Time
Impact Velocity From Given Height
Viewing g as the value of Earth's Gravitational Field Near the Surface

Average Velocity for Constant Acceleration Calculating average velocity when acceleration is constant

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Average Velocity for Constant Acceleration

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The goal of this video is to explore some of the concepts or
formulas you might see in the traditional Physics class but
even more importantly to see that they are just common
sense ideas.
So let's just start with a simple example.
Let's say that, and for the sake of this video just so don't
have to keep saying this is the magnitude of the velocity,
this is the direction of the velocity, et cetera.
Let's just assume that if I have positive number that it means
for example if I have a positive velocity it means that I am
going to the right and let's say if I have a negative number
which we won't see in this video, let's assume that I'm going
to the left and that way I can just write a number down -we're
only operating in one dimension- you know that it is
specifying with the magnitude and the direction.
If I said that the velocity was 5 metres per second that
means 5 metres per second to the right.
If I said it is negative 5 metres per second that means
it's 5 metres per second to the left.
Now let's just say, just for a simplicity, let's just say that if we
start with an initial velocity, we start with an initial velocity of
5 meters per second
Once again I am specifying with a magnitude and the direction
because of this convention
Here we know it is to the right
and let's say that we have a constant acceleration
we have a constant acceleration at play
of 2 meters per second per second, or 2 m/s^2
and once again since this is positive, it is, to the right
and let's say that we do this for a duration
so my change in time is...let's say we do this for a duration of 4 s
so *s* for this video is seconds
So what I want to do is think about how far
how far do we travel?
Well there's two things here.
How far or how fast are we going, after 4 seconds
and how far have we traveled over the course of those 4 seconds
So let's draw ourselves a little bit of a diagram here
so this is my velocity axis
and this over here is my time axis
(let me draw a straighter line than that)
so that is my time axis
This is velocity, that is my velocity right over there
and I'm starting off at 5 m/s
this is 5 m/s right over here
so V_i is equal to 5 m/s
and then every second that goes by, I'm going 2 m/s faster
because it's 2 meters per second per second!
so every second that goes by
so after 1 second...I'm going to go 2 m/s faster...so I'll be at 7
Or another way to think about it
is the slope of this velocity line is my constant acceleration
I have a constant slope here
So it might look something like that
So what has happened after 4 seconds?
so 1...2...3...4...so this is my delta t
So my final velocity is going to be right over there
(I'll write it down here because it's getting in the way of this word *velocity*)
And so this is V_f, this is my final velocity
and what would it be?
Well I'm starting at 5 m/s, so I'm going to do it both ways...
using the variables and using the concrete numbers
So I'm starting at some initial velocity
the subscript *i* says *i* for *initial*
And then each second that goes by, I'm getting this much faster
So if I want to see how much faster have I gone
I multiply the number of seconds that go by times my acceleration
And once again, this right here
I just wrote the subscript *c* saying it's a constant acceleration
And so that will tell me how fast I've gone
If I start at this point, and I multiply the duration times my slope
I will get this high, I will get to my final velocity
and just to make it clear with the numbers
These numbers really could be anything

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When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831...

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At 2:33, Sal says "double bonds" but should say "single bonds."

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