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No steelers versus vectors battle royal citizens for replacement with

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ten grand just like we can't be negative displacement can

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be his basement requires direction that's considered positive there's in

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victor's a numerical value on it so one dimensional vectors

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have value for magnitude and direction that's philosophy inspector uses

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displacement average last year a single more fun with units

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you need to be the same when adding subtracting easy

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when using metric system imperial system in it so easy

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for you nick Using a girl all right let's do

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this physic can be tough right Lots of setting up

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experiments tracking data and crunching numbers we think it's time

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to take a vacation off on a plane find a

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nice beach somewhere ten thousand kilometers away that's the life

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but sadly all the occasion must end and we've got

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to come back to the real world so here's a

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question How far did we travel Sure we can say

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the total distance traveled with twenty thousand kilometers but we're

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back where we started So in the long run was

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there any real change in our position Yep There's physics

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making stuff complicated again Sadly we don't actually get to

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go to the beach but our imaginary trip lets us

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look at the difference between distance and displacement know you

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may have heard about displacement in terms of a submerged

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object displacing fluid but it means something totally different here

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Distance is pretty understandable We talked about distance all the

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time like if we run a ten k race even

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if we go in a circle and end up back

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where we started we still ran ten kilometers are fitness

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tracker wouldn't lie to us so distance is just a

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measurement The total amount traveled but displacement is different displacement

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measures how far we are from a c starting point

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So if you run that ten k and finished back

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at the starting line are displacement is in ten kilometers

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in fact it zero kilometers no matter how sweaty we

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might be and what would our displacement be past the

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finish line In other words behind the starting point in

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that case are displacement would have a negative value It

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really depends on which direction we've chosen to be positive

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when we're setting up a vector map we can think

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of ourselves as an observer and will pick which direction

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To face an emotion going in the same direction we're

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facing will be positive and in emotion in the other

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direction will be negative now in america distance can never

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be negative There's no such thing as a negative ten

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k even if he ran backwards Distance is a scaler

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measurement A scaler quantity is something that has a numerical

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value known as magnitude Think wait or area or value

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or flying ten thousand kilometers and back anything that could

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be quantified as just a number vectors are different Vector

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is a measurement that has both of value and a

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direction that covers things like heat flow or forces or

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you guessed it displacement so on our vacation are total

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displacement by the end of the round trip would be

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nothing zilch Zero nothing to show for it but beach

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sell fees vectors can depend on who's doing the measurement

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also like if we're playing catch with a friend when

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you throw the ball it's moving at a certain speed

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away from you and that would be positive velocity relative

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to your position But it's coming right at your buddy

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and at a negative velocity relative to his position so

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he better be paying attention You want to avoid stopping

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any velocity with your face doing that with scaler quantities

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is easy Since a scaler is the same thing as

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a number we can just add subtract divide you name

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it Math with vectors can get tricky though you can't

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really multiply up times left For example For now we'll

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stick with one dimension of movement and we'll dig into

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the multidimensional stuff later Because vectors involved movement we usually

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see them drawn as an arrow The length of a

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narrow indicates the vectors magnitude and the direction of the

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arrow indicates well the direction of the vector here's an

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example of a vector diagram of an airflow We can

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see that there are different directions for the force is

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involved and we can see that there's a pattern to

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the forces Also we can see that we need to

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find a basement and hunger down How can we tell

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that something in an equation is a vector Usually it'll

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have a narrow over it like this Otherwise you might

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see it written in italics or bold it and sometimes

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we might see a plus or minus sign in front

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Of a number Just make sure that when you're writing

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a vector make it clear jesse's distance and displacement are

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related so our speed and velocity the difference velocity is

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a vector quantity and speed is a scaler meaning velocity

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has a direction and the equations to calculate them are

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almost the same too Speed equals the change in distance

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over the change in time's and velocity equals the change

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in displacement over the change in time Distance is always

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a positive number so speed is always positive too Like

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in the real world you can't travel backwards in time

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When sheldon comes up with something to time travel then

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we can revisit the negative sign their velocity Now it

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can be negative if the displacement is negative When we're

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dealing with displacement we always have to make sure that

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we're paying attention to the starting value because displacement doesn't

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have to start at zero let's say your dog is

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hanging out in the park right Oh spots a squirrel

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twenty meters away and it's on mr squirrel makes a

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dash for the tree forty meters away from fido and

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it's a lucky day for the rodent who gets there

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Just before the pooch and we'll say it took them

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both about five seconds Calculating the velocity for your dog

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would be pretty straightforward The change in distance is forty

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meters and the change in time is five seconds His

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velocity for this strip would be eight meters per second

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But the squirrel is slower because from the start he

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already had a displacement of twenty meters relative to your

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best friend So we have to subtract the initial displacement

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from the final displacement and we've got to remember to

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do that any time the initial displacement isn't zero so

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when we do the math we find that the squirrels

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velocity is four meters per second and yet he still

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has the gall to taunt fire just like velocity can

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change based off of our position The value of velocity

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can change based off of what we're looking for like

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average versus instantaneous For example let's go backto our plane

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trip How far away did we say that Beach wass

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ten thousand kilometers that's about the distance from los angeles

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to new zealand So let's say it takes us fifteen

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hours to get there That means our velocity for the

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whole trip would average ten thousand kilometers divided by fifteen

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hours or about six hundred sixty seven kilometers per hour

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to the southwest But what if we have to stop

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in fiji to re fuel What would our velocity be

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at that point in time It would be zero in

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no direction at all Just sitting on the tarmac playing

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candy crush for the twelve straight our that's the difference

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between average velocity and instantaneous velocity average velocity covers the

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whole time period Instantaneous philosophy is just for one moment

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in the time period both are useful We just need

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to make sure we know which one we're looking for

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When it comes to velocity It's also important to know

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the difference between constant and average let's say instead of

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having to re fuel were able to catch a nonstop

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flight instead and just help ourselves think we'll say this

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is a magic plane that always has the exact same

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velocity Let's say that eight hundred kilometres to the southwest

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what's our velocity an hour into the flight eight hundred

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kilometres at our nine Yep That's right Eight hundred Constant

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velocity means that at any point in time the total

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change in displacement divided by the total change in time

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will equal the same number as we've seen that's not

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necessarily the case for average velocity Okay so let's put

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some of this speed of velocity step to the test

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with something that's a little less straightforward literally lets say

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its errand day we need to go to the grocery

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store and grab a few things The grocery store is

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five kilometers to the west of our house and it

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takes us ten minutes to get there nothing but green

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lights for this trip but all that shop and makes

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us hungry So instead of going home we get some

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tacos from our favorite taco joint that's two kilometers to

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the east of our house This part of the trip

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from the store to our delicious snack takes twelve minutes

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and we're going to say that east is the positive

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direction for all this Now we can run some numbers

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and we want those numbers to be in terms of

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meters seconds and meters per second We're going to find

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out the average velocity for the first part of the

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trip the average speed for the first part of the

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trip the distance for the whole trip the displacement for

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the whole trip and the average velocity and average speed

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for the whole thing too got it So the first

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part of the trip took us five kilometers to the

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west over ten minutes remember the equation for velocity is

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this velocity equals the final displacement minus the initial displacement

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over the final time minus the initial time and since

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we want are answers to be in meters per second

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let's do our conversion now before we forget so we'll

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change five kilometres to five thousand meters and ten minutes

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to six hundred seconds and because east is our positive

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direction that makes west the negative direction since our starting

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displacement and starting time we're both zero now our equation

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looks like this velocity equals negative five thousand meters minus

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zero meters divided by six hundred seconds meaning our velocity

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for the first part of trip was negative Eight point

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three three meters per second as far as our speed

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Well the distance is the same as the displacement for

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this first leg of our journey and we've already done

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the math since distance can't be negative we don't have

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to change it to positive easy enough that makes our

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average speed for this part eight point three three meters

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per second now let's go to the displacement for the

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whole trip displacement equals the final displacement minus the starting

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replacement pretty simple our final taco based displacement was two

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kilometers in the positive direction starting displacement a big fat

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zero but we still want to work in terms of

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meters so we've got two thousand meters on her hands

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or to put it scientifically to point zero zero times

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ten to the third meter's distance involves a little more

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attention because we've got to account for all the ground

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we covered So at the start we went five kilometers

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west and we ended up with two kilometers to the

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east of our starting point meaning the second part of

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our trip covered seven kilometers adding it up we find

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a total distance of twelve kilometers also known as one

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point two zero times ten to the fourth meters using

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the right amount of sig six that's a big difference

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from the displacement isn't it We're moving right along here

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huh We might not even have time for a second

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Round of taco goodness let's calculate the average velocity for

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our trip We said the total displacement was two thousand

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meters now we need the total time The second part

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of the trip took twelve minutes which is seven hundred

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twenty seconds Add that to the six hundred seconds the

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first leg took us on Our total travel time was

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one thousand three hundred twenty seconds Divide displacement by time

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and we have an average velocity of one point five

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two meters per second The equation for speed is total

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distance divided by time A total distance Twelve thousand meters

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total time is still one thousand three hundred twenty seconds

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Do the division and we get an average speed of

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nine point zero Nine meters per second huh Our speed

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is a lot more impressive than our velocity So even

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though the two words might mean the same thing in

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the non physics world when it comes to science speed

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and velocity can be very different As we worked on

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this problem you saw that we had to convert units

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Luckily a lot of the conversion was kilometers two meters

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conversion in the metric system is super easy because it's

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usually just a matter of changing the order of magnitude

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but in america we still use the imperial system most

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of the time which is a little bit less intuitive

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Twelve inches in a foot five thousand two hundred eighty

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feet in the mile Nothing intuitive about that at all

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It's like a bunch of old english guys just threw

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darts at some numbers to come up with these measurements

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Yeah that story about a king using his foot to

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come up with the measurement for an official foot old

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wives tale Not really So we need a more intuitive

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way to handle these conversions One way to help ourselves

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out is by using a grid let's say we want

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to convert twenty five miles per hour two meters per

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second The first part of our grid will look like

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this We're going to be using multiplication and division in

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this process so we'll put the things we multiply on

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top of the grit and the things we're going to

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divide on the bottom So let's focus on the our

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unit because we're going to be dividing that bad boy

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The first step to get two seconds is to divide

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An hour in two minutes will add a new section

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to our grid and put one hour on top and

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sixty seconds on the bottom Then we'll attack more to

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the grid and split a minute into sixty seconds Okay

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so we've got into one of the units we need

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to do this Conversions let's go after meters now there's

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about one point six kilometers for each mile we'll throw

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that onto the grid also Now we just have to

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break up a kilometer and two meters and there are

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precisely one thousand meters in each kilometre looking at our

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grid it looks like one big division problem We've got

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our dividend on top and our divisor on the bottom

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So how about we put together an equation We'll apply

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all the numbers on the top and multiply all the

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numbers on the bottom leading us with forty thousand meters

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on top and three thousand six hundred seconds on the

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bottom Doing that last piece of division we find that

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twenty five miles per hour equals eleven point one meters

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per second We do have to take the conversion step

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by step and step by step would probably convert about

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half a meter per second Sorry i want to get

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started with the conversion stuff It can be pretty hard

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to stop So just remember speed and velocity Make sure

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you're choosing the right one for whichever problem you're trying

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to solve just like distance and displacement speed and velocity

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related But they're not the same Kind of like you

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and your family except for that one year and there 00:14:02.064 --> [endTime] is no way you share any dna with her

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