ShmoopTube

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smell let's get moving intro to acceleration on acceleration is [writing on chalk board]

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velocity into laughs after knowledge direction or future the loss of rep

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alright next the acceleration before your very eyes along even in time grass

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the grass picture our ups and downs of acceleration ok acceleration it's one of

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my favorite things who doesn't want the thrill of putting the pedal to the metal [man in racing car]

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and pee to your seat and it's no surprise to learn that acceleration is

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related to velocity so buckle up kids it's time for the only thing more

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exciting than the Indy 500 graphs we'll actually get some graphs in a minute [car race]

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let's dive deeper into that relationship between velocity and acceleration first

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well actually what the heck is acceleration scientifically speaking

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acceleration is a description of how an object's velocity is changing over time [writing on chalk board]

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and we're going to be looking at uniform acceleration it doesn't mean an [policemen in uniform

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acceleration that's dressed in blue and wearing a badge

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it means acceleration that stays the same for an extended period of time

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like the instant an airplane first revs its engine [airplane on runway]

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taking off down the runway it doesn't go from sitting on the runway to flying in

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the blink of an eye the engine provides uniform acceleration so the plane picks

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up speed second by second until it's fast enough to get airborne or think of [airplane takes off]

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a snowboarder at the top of the hill when they first hit the slope they're

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barely moving but the acceleration of gravity gets them going faster and

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faster until they reach a force of negative acceleration known as a treat [snowboarder hits tree]

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yeah uniform acceleration is easier to wrap our minds around and makes the math

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easier too an easy math is our favorite kind of math right back the velocity

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velocity can tell us how fast we're going at a specific moment in time or [writing on chalk board]

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how fast we went in the past like if you're in a car going 40 miles an hour

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that's velocity or a turtle crawls from 10 seconds covering one meter yeah and [tortoise walking around]

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because it's a vector a quantity that has a value and a direction it also

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tells us the direction of that motion well acceleration can tell us how fast

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we'll be going in the future it's like having a psychic for speed and since

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it's also a vector the direction part is in there too okay so here we go the [psychic with a crystal ball]

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velocity equation velocity equals the change in displacement divided by the [writing on chalk board]

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change in time think distance over time we've seen this equation before the

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equation or acceleration looks pretty similar yeah

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see we have to just change couple letters their acceleration equals the

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change in velocity divided by the change in time so if the velocity of a biker

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starting up his hog changes from zero liters per second to five meters per

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second and that change takes place over ten seconds then the bikers acceleration

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would be 0.5 meters per second squared and because acceleration and velocity

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are related you might think we can just sub in the equation for velocity and

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everything would be great but it's not quite that easy because it involves a

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calculus yeah all right so here's the equation for acceleration in terms of

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displacement acceleration equals two times the quotient of the change in

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displacement over the change in time change in time is squared here well this

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equation only works when the initial velocity is zero by the way so when you

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think initial velocity think some guys sitting on this couch first it kicks [man sitting on couch]

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everything off it's not even getting up to grab a bowl of pretzels all right

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well before we tackle acceleration versus time graphs let's make sure we [race car driver in rose garden]

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have a good handle on a velocity versus time first suppose we're taking our

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beloved princess Rigoletto for a walk now the princess prefers a leisurely [race car driver with a pig on a leash]

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stroll rather than a vigorous jog so we're covering a meter per second here's

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a displacement versus time graph that shows the first 10 seconds of the walk

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before princess picolet oh we didn't anyway take a break take a look at this

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distance versus time graph we can see here that an object moved 10 meters in

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the positive direction over 10 seconds since velocity equals the change in [graph on screen]

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displacement over the change in x we can see pretty clearly that the velocity is

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1 meter per second and well another way of putting it is that velocity equals

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the slop or a slope of this line since slope equals rise over run which is the

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change in the y-axis over the change in the x axis in this case the y axis is

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displacement and the x axis is time and since this is a straight line we can

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also see that the velocity is constant well this object doesn't speed up or

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slow down in its little journey here it keeps right on going at the same

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speed so what would our velocity versus time graph look like

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well it'd look like this one nice and flat some might even say boring so what

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does this graph tell us about our Piggy's acceleration well remember

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acceleration is the change in velocity over time does the velocity change nope

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not one bit there is no acceleration the pig is on cruise control just cruising

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along no accelerating well that's no fun and like I've been talking about

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acceleration this whole time Paul and our [pig sits down]

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Graff has none at all alright let's take care of that here's another displacement

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versus time graph what is this graph telling us well for one thing that it's [graph on screen]

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happy but more importantly it says that we've got something that starts at the

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zero position move 25 meters in the negative direction then it comes back

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moving in the positive direction when would this happen well let's say you

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want to have a little game of catch but all your friends are busy doing lame [family playing piano together]

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stuff like you know spending time with their family or studying

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look friends are the word but there's a solution it's boomerang time yes the

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boomerang the perfect outdoor toy for the anti-social trust us we've been [man playing with a boomerang]

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there that we started shmoop on a graph we know we have motion and we know the

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slope isn't constant that's definitely not a straight line well what does this

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mean about the velocity well the object slows down for the first 5 seconds

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eventually coming to a stop then on its return trip it picks up speed so the [graph on screen with boomerang]

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velocity isn't constant either now let's start by figuring out this whole

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velocity thing well start it one second right there remember to find the

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instantaneous velocity the velocity at any one point in the time span we have

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to look at the displacement at the moment right after our target second and

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from that we'll subtract the displacement from the moment right

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before oh it's dark net second one rather than second zero because we

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started at second zero we have to look at second one and second negative one

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sadly there was no way to go back in time even for a second so that wouldn't

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work out very well would it the displacement at second two is negative

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16 meters that second zero the displacement is zero instantaneous

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velocity is an average well the change in time we're looking at is two seconds [writing on chalk board]

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and the change in displacement is negative 16 meters so a second one the

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velocity is negative eight meters per second let's plot that on our graph

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right there all right now let's look at the velocity at the second second or

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second two and that's less confusing and we'll do the same thing subtracting the

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displacement at second three which is negative 21 meters from the displacement

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from second one which is negative nine meters giving us a change in

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displacement of negative 12 meters and a change in time of two seconds making the

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velocity negative meters-per-second here and we can pop

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that onto our graph well we can do this all day but we won't make you listen to

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us plot each and every point and I will still look we'll still do it later for

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fun but you won't have to listen to it eventually we have a velocity graph that

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looks like this oh and how do we graph the velocity from second zero to second

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one well this is a straight line and there's no reason to think that

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something crazy happened during that first second to knock this line off its

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path so we can just extend it back to be a zero point like so so what does this

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velocity graph tell us well it tells us that the boomerang started off quickly

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in the negative direction slowed down stopped for a moment then started back

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in the positive direction getting faster pretty much the same thing as a

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displacement graph which makes sense since they're related at all but what

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does this graph tell us about acceleration remember acceleration is

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the change in velocity over the change in time our final velocity is 10 meters [writing on chalk board]

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a second and our starting velocity was negative 10 meters a second making the

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total change 20 meters a second and that was over a 10 second period which makes

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the acceleration 2 meters per second per second or to put it another way 2 meters

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per second squared it might seem a little weird that even as this object is

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slowing down its acceleration is staying the same

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it might help think of gravity gravity is a constant force of acceleration

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negative 9.8 meters per second squared well let's say we're throwing a ball

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straight up in the air why because everyone gets bored sometimes even [race car driver hits ball up into sky]

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racecar drivers once the ball leaves our hand the acceleration of gravity starts

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working right away it slows the ball down and sends it back down our way so

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the ball speed and velocity are changing but the acceleration of gravity is not

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when we had a displacement graph that was linear that meant the velocity was [graph on screen]

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constant resulting in a graph that had no slope nothing a dead man's balls and

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the same thing applies between velocity graphs and acceleration graphs if a

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velocity versus time graph is linear like this one the acceleration graph

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that goes along with it will also be flat and we can tell if acceleration is

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positive or negative by looking at the slope of the velocity graph

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if a slope of the velocity line is positive the acceleration is positive if

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the slope is negative well yep so is the acceleration

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now you might have heard the term deceleration somewhere maybe in some

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sci-fi movie with giant ants we're gonna ask you to do us a favor forget that

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word at least when you walk into your science class in physics there's no such

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thing as deceleration acceleration is a vector quantity which means it can be

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positive or negative but just because an object has a negative acceleration [writing on chalk board]

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doesn't mean it's slowing down it depends on its direction if an object

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has velocity in the negative direction and negative acceleration well that

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means the object is speeding up but velocity in the positive direction and

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negative acceleration yeah that means it's slowing down as does velocity in

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the positive direction and negative acceleration and if both the direction

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of velocity and acceleration are positive it means that the object is

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speeding up as it goes along well to boil it down of the directional velocity

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and the acceleration share the same sign whether positive or negative it means

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the speed is increasing if they conflict with one plus and the other minus this

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means the object is slowing down yeah you might notice that we haven't

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actually seen an acceleration versus time graph don't don't worry we've got

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plenty of those coming up just not in this lesson it's more important for now [man racing in a car]

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that you understand how velocity and acceleration are related when we step on

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the gas pedal our rate of velocity changes say we have a constant

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acceleration of five meters per second squared

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five seconds into this motion we're covering 25 meters a second not bad

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that's about 56 our there but after 15 seconds of this

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constant acceleration but we're traveling 75 meters a second

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that's almost 168 miles an hour which just might win us a race or get us a

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ticket [race car gets pulled over by police]

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