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- [Instructor] In this video
we're going to go through

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a few examples of setting up some problems

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with constant acceleration.

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We're not going to solve them,

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we're just going to look at what we know

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and what the question is asking for

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and then identify which one
of these equations over here

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will be the most useful
for helping us solve it.

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So before we jump into the examples,

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I wanna say that it is very important to

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understand where these equations come from

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to really develop a
strong understanding of

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position and velocity
and acceleration and time

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and how they're all
related to one another.

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And Sal has a lot of
videos that go through that

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and can help you build that understanding.

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But once you have that understanding,

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these equations are kind of
like using a calculator where

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they help you save time.

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It's important to

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know how to add, subtract,
to multiply and divide,

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so you know what a calculator
is doing when you use it.

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But once you understand that,

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the calculator is a really valuable tool.

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And that's what these equations are like,

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they're tools that we can
use when we understand

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where they come from.

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With that out of the way, let's
dive into our example here.

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So the question says,

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"A light rail commuter train

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"accelerates at a rate of 1.35
meters per second squared.

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"How long does it take
to reach its top speed

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"of 80 kilometers per
hour starting from rest?"

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All right, so let's unpack
this and see what it's saying.

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So let's just start at the beginning.

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A light rail commuter train accelerates

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at a rate of 1.35 meters
per second squared.

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So that's pretty direct,

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it's just telling us
what the acceleration is.

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So let's write that down.

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The acceleration is 1.35

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meters per second squared.

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All right, there's one thing.

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Okay, so let's keep going.

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How long does it take
to reach its top speed

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of 80 kilometers per
hour starting from rest?

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So that one's a little
bit more complicated,

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there's more going on in here.

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But if we just start at
the beginning and say,

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"How long does it take?"

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That by itself is a question.

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There's some more stuff afterward,

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but that by itself is just
asking about the time,

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how long does it take?

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All right, so let's note that
by circling this time here.

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We don't know what it is yet,
but this is our question,

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we're being asked about the time.

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All right, so if we keep going here,

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we get, all right,

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how long does it take
to reach its top speed

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of 80 kilometers per hour?

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That's saying its top speed
is 80 kilometers per hour.

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When it's done speeding up,

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it'll be going at 80 kilometers per hour.

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So that's the final velocity

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or just our velocity at the time here.

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So that's 80 kilometers per hour.

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80.0 kilometers per hour.

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And sometimes you'll see this
right here written as V sub f

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to really explicitly say
it's the final velocity.

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So the notation might vary
in your physics class.

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Whatever notation you use, that's fine,

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but make sure to ask
yourself what is this symbol

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really talking about.

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So anyway, 80 kilometers per hour,

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per hour.

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Okay.

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And so we have that.

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And then if we keep going,

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it says, "Starting from rest."

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So that's saying that at the
beginning when it starts,

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it's at rest, which means it has

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zero for it's initial velocity,

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it's just sitting there.

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So let's fill that in,

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that's zero meters per second.

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Okay.

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So we had analyzed this question

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and we see that, actually,

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the change in distance didn't appear

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anywhere in this question,

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it's just these four values right here.

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So let's see if we can
look at these equations

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and identify one that
has all of these things

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and doesn't have delta x,

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since we don't know delta x

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and we're not looking for it either.

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So we see these two have delta x here

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so we can rule those out.

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And this one also has a delta
x so we can rule that out.

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So that leaves this one.

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Let's see, it has velocity,
the final velocity here,

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it has the initial velocity here,

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it has acceleration here,

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and then it also has time which
is what we're looking for.

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So we can use this.

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We've figured out that for
this question right here,

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we can just use that top equation.

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All right, and then to continue this

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we would plug in numbers
and then solve for t

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and see what that time indeed is.

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So for this video,

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we're not going to have
to go through that,

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we're just going to go through another

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example of setting things up.

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So let's go down to this
question right here.

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While entering a freeway,
a car accelerates from rest

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at a rate of 2.40 meters
per second squared

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for 12.0 seconds.

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How far does the car travel
during those 12 seconds

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and what is the car's final velocity?

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So this one actually asks two questions.

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Let's just focus on the
first one to begin with,

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and also let's see what we know.

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So while entering a freeway,
a car accelerates from rest

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at a rate of 2.40 meter
per second for 12 seconds.

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So there's a lot of information
here in this first sentence.

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So let's see, it says,

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"Accelerates from rest," right
here, accelerates from rest.

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That tells us that the initial
velocity is zero, right?

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From rest, it wasn't moving initially,

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it was at rest.

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So let's write that down.

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This also, just like the previous example,

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had an initial velocity
of zero meters per second.

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That's not always the case,

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but it happens that in
these two examples it was.

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So let's keep going.

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So it accelerates from rest

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at a rate of 2.40 meters
per second squared.

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So that's telling us
what the acceleration is,

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2.40 meters per second squared.

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So let's write that down, 2.40
meters per second squared,

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meters per second squared.

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And in all of these problems,
it's important to think about

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whether something is moving

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in the positive direction
or in the negative direction

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or if it's accelerating
in the positive direction

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or the negative direction.

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It actually looks like for these examples

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we've chosen everything is

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moving in the positive direction

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and accelerating in that same direction.

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So we won't have any
negative signs pop up,

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but it is important to think about that

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when you're doing these kinds of things,

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just in case something is negative

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and that does affect your
answer and what's going on.

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But anyway, so it's accelerating forward,

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everything is going in the same direction.

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So we're thinking of the forward
as the positive direction

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and they're accelerating, this car,

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is accelerating at 2.40
meters per second squared.

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All right, and it says also

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that it's doing that for 12.0 seconds.

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So we can write that down as well,

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12.0 seconds.

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All right, so we know three things here.

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And you'll find that
in problems like this,

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that's the magic number.

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Once you have three of these,

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you can find out the other
pieces using these equations.

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Anyway, so the first question says,

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"How far does the car travel
during those 12.0 seconds?"

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Well, it's asking how far,

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so that's going to be the delta x here,

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this change in position.

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How far does it travel
during those 12 seconds?

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It's going to be this value right here.

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So this is our question,

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circle it here.

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So now notice we don't have this,

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so we can look for an
equation that doesn't have

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this final velocity value in it

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and then that will be an equation that

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will hopefully have these other four,

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but we'll have to check that.

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This one has that final velocity in it,

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so we can rule that out.

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I see this one also
has the final velocity.

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This one doesn't have the final velocity.

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So let's look at that.

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So it has the position,
the change in position,

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that's what we're looking
for, it has it right there.

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The initial velocity is right here,

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so we have that as well.

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Let's see, it has time
in it and we have time,

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so we will be able to plug that in.

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And then finally, it
also has acceleration.

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So it has everything we need,

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it has the thing we're looking for,

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and it doesn't include anything
that we just don't know,

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that we're not even looking for.

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So we found that for
this problem right here.

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This second equation here is going to be

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the one that is most useful
for answering the question,

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"How far does the car travel
during those 12 seconds?"

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So that's for that question,
but this block here

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actually has a second question.

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Maybe I'll switch to green.

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Let's look at this question.

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What is the car's final velocity?

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All right, so that means
we're looking for this now.

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Right here, what's this?

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Well, we've already identified

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these different pieces that we know,

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and if we did the first
part of the problem,

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we would actually have a
value for delta x here.

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But assuming we didn't find that yet,

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we could look at this and say,

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"What's the car's final velocity?

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"I want to look for
something that has V in it

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"and has these other
three things that I know."

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And if you look and
you check through here,

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let's see, what is it?

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So, yeah, it would actually
end up being this one again.

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This is that equation that doesn't have

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the change in position in it.

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And so just using the green color,

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I'll underline this here to say that

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this equation is useful for this question.

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And actually, now that we have this value,

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we could've used really any
of them that had our V in it.

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So our options open up

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once we know more than
three different things.

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But anyway, hopefully going through

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a couple of these examples

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will be helpful for you when
you run into your own questions

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and have to think through,
"Okay, what do I have,

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"What am I looking for,

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"and which equation will help me

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"move forward and solve this question?"