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Physics Videos 34 videos

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Physics: Let's Get Moving: Introduction to Acceleration 8 Views


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Description:

An introduction to acceleration à la Shmoop.

Language:
English Language
Subjects:

Transcript

00:00

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

00:08

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

00:13

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

00:17

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

00:30

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

00:34

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

00:38

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

00:43

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

00:50

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

00:54

well actually what the heck is acceleration scientifically speaking

00:58

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

01:02

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

01:07

acceleration that's dressed in blue and wearing a badge

01:10

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

01:14

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

01:17

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

01:22

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

01:27

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

01:32

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

01:35

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

01:40

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

01:45

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

01:50

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

01:55

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

01:59

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

02:04

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

02:09

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

02:13

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

02:18

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

02:23

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

02:27

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

02:34

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

02:40

equation or acceleration looks pretty similar yeah

02:43

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

02:47

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

02:52

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

02:56

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

03:01

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

03:07

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

03:12

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

03:16

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

03:21

displacement acceleration equals two times the quotient of the change in

03:25

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

03:30

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

03:34

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

03:38

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

03:43

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

03:46

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

03:50

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

03:55

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

04:00

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

04:04

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

04:10

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

04:15

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

04:19

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

04:24

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

04:29

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

04:35

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

04:41

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

04:46

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

04:51

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

04:54

speed so what would our velocity versus time graph look like

04:58

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

05:03

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

05:06

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

05:11

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

05:17

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

05:21

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

05:23

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

05:27

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

05:31

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

05:35

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

05:39

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

05:43

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

05:46

stuff like you know spending time with their family or studying

05:50

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

05:55

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

05:58

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

06:03

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

06:07

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

06:11

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

06:16

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

06:19

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

06:24

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

06:28

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

06:33

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

06:36

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

06:40

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

06:44

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

06:48

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

06:52

16 meters that second zero the displacement is zero instantaneous

06:56

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

07:01

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

07:05

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

07:09

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

07:14

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

07:18

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

07:23

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

07:27

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

07:32

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

07:35

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

07:39

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

07:44

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

07:49

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

07:54

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

07:56

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

08:00

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

08:05

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

08:09

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

08:13

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

08:16

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

08:20

does this graph tell us about acceleration remember acceleration is

08:24

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

08:29

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

08:33

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

08:38

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

08:43

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

08:48

slowing down its acceleration is staying the same

08:51

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

08:56

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

09:01

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

09:04

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

09:08

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

09:13

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

09:17

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

09:22

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

09:27

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

09:32

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

09:36

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

09:41

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

09:44

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

09:48

the slope is negative well yep so is the acceleration

09:51

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

09:55

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

09:59

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

10:03

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

10:09

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

10:13

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

10:18

has velocity in the negative direction and negative acceleration well that

10:22

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

10:26

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

10:31

the positive direction and negative acceleration and if both the direction

10:34

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

10:39

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

10:42

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

10:46

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

10:52

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

10:56

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

11:00

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

11:03

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

11:08

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

11:12

acceleration of five meters per second squared

11:14

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

11:18

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

11:23

constant acceleration but we're traveling 75 meters a second

11:27

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

11:33

ticket [race car gets pulled over by police]

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