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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.
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]
Full Transcript
- 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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