Velocity Time Graphs, Acceleration & Position Time Graphs - Physics - Free Educational videos for Students in K-12

Velocity Time Graphs, Acceleration & Position Time Graphs - Physics - By The Organic Chemistry Tutor

Transcript


00:00	in this video , we're gonna go over motion graphs
00:03	. We're gonna talk about position , time graphs ,
00:05	velocity , time graphs and acceleration time graphs . Now
00:10	there's two concepts that need to be familiar with the
00:13	slope in the area . The slope is associated with
00:17	division . The area is associated with multiplication . Perhaps
00:23	an algebra . You've seen the slope represented by the
00:26	letter M . The slope is calculated by dividing the
00:32	change in Y by the change in X . So
00:36	when you're calculating slope , you're using division . Now
00:40	, let's say if we want to find the area
00:43	as This rectangular segment , Let's call it segment two
00:49	. Mhm . To find the area , we need
00:52	to multiply the less by the west . In this
00:56	case we're multiplying the Y values by the X values
01:00	. So this would be the change in X .
01:02	That would be like the whiff of that rectangle .
01:06	And this is the change in Y . Which would
01:08	be the height of the rectangle . If we multiply
01:10	those two , that will give us area . So
01:14	associate area with multiplication , but slope with division .
01:22	In algebra you've seen this equation for slope , It's
01:25	the change in Y . Which is Y tu minus
01:28	Y . One divided by the change in X ,
01:31	which is X two -X . 1 . And you've
01:34	seen this equation for area areas , lifetimes with Wendell
01:38	from rectangle . So make sure you understand those concepts
01:43	. Now let's consider three common time graphs that you
01:46	can encounter . The 1st 1 is the position time
01:49	graph . Typically it's going to be X versus team
01:52	. So when you see that you're dealing with motion
01:54	along the X axis , it could be why versus
01:57	T . If you're dealing with motion along the Y
01:59	axis , vi versus T . Is a velocity time
02:03	graph A versus T . Is the acceleration time graph
02:09	. Now , what do you think the slope of
02:12	a position time graph represents ? Remember slope is the
02:18	change in Y over the change in next . You're
02:20	dealing with division . So if we were to divide
02:24	the position or the change position by the change in
02:27	time , what will we get ? The change in
02:31	position ? Divided by the change in time ? The
02:35	change of position is displacement . If you defied displacement
02:41	, let me just put D for displaced instead of
02:42	writing everything out . But if you were to divide
02:45	displacement by time , you're gonna get the velocity .
02:49	So the slope of a position time graph represents the
02:53	velocity or the instantaneous velocity at that instant . Mhm
03:00	. Mhm . If you calculate the slope that at
03:05	least like an added tangent , you're gonna get an
03:06	instantaneous velocity . If you calculate the slope used in
03:10	two points , you're gonna get an average velocity by
03:15	the way , calculating the slope . At one point
03:18	, it's like finding the slope of the tangent line
03:20	that will give you the instantaneous velocity , calculating the
03:23	slope using two points which is the slope of the
03:25	secret line that will give you the average velocity .
03:29	Nevertheless , the slope of the position time graph gives
03:32	you velocity . So make sure you understand that .
03:36	They might be wondering what is the area of a
03:40	position time graph tells us . The area doesn't tell
03:44	us anything . Remember area is associated with multiplication .
03:50	If we were to multiply the y axis by the
03:53	X axis in this case the change in acts by
03:57	the change in T . We would get meters time
03:59	seconds , which it really doesn't help us in physics
04:04	. So the area for position time draft is not
04:07	really helpful . Yeah . Now , what about the
04:10	velocity time graph ? What does the slope tell us
04:15	? Yeah . Well , in order to find out
04:17	the slope of velocity time graph , we need to
04:20	use division If we were to divide V by T
04:25	. If we were to take the change in velocity
04:27	and divided by the change in time , what will
04:30	we get velocity typically has a unit to meet us
04:34	for a second . And time is usually in seconds
04:38	. When you divide these two , you get the
04:40	units meters per second squared , what is variable or
04:46	term is associated with the units meters per second squared
04:50	from physics , you've likely seen it as acceleration .
04:54	The slope of a velocity time graph is the acceleration
05:01	. So that's what you need to know when dealing
05:02	with the VT graph . Now , what about area
05:09	? What does the area of a velocity time graph
05:11	tell you ? So , once again , when you
05:14	think of area think of multiplication . If we were
05:17	to multiply the Y axis by the X axis .
05:21	If we were to multiply V by T , what
05:24	will we get ? Well , let's look at the
05:27	units . Velocity is usually in meters or per second
05:31	or meters over seconds . Time is usually in seconds
05:35	. When you multiply these two , the unit seconds
05:38	cancels . And so we get the unit meters ,
05:41	meters is the unit for distance position , displacement .
05:48	But it turns out that when you multiply velocity by
05:51	time you get specifically displacement . So I'm going to
05:55	put dif a displacement speed multiplied by time is distance
05:59	velocity times , time is displacement . So the area
06:04	of a velocity time graph is specifically displacement . Mhm
06:12	. So when dealing with a velocity time graph ,
06:14	the acceleration , I mean the slope and the area
06:16	is important . The slope is the acceleration . The
06:20	area is the displacement , displacement is the final position
06:25	, modesty initial position . If you move this term
06:29	to the other side , you're going to get this
06:31	familiar equation . X final is equal to X initial
06:34	plus VT . Let me erase that because I'm going
06:39	to need the space on the right side . So
06:43	hopefully you're taking notes and writing these things down because
06:47	we're gonna use this later in the video . Now
06:50	let's move on to the acceleration time graph . What
06:53	is the slope Of an 80 graph represent ? Wow
06:58	, let's divide . Why buy X . So on
07:04	the Y axis we have acceleration on the X axis
07:08	. We have time . So what is the rate
07:11	of change of acceleration now for most physics classes that
07:16	you're going to counter , you're not going to have
07:18	to worry about it . This is not going to
07:20	be applicable to the everyday common situation . But some
07:24	physics course they do have a value for this and
07:29	this represents a jerk or joke . You can look
07:32	this up in Wikipedia you may see in some textbooks
07:36	, but that's the slope of an acceleration time graph
07:40	on a physics test . If you're asked the question
07:43	, what is the slope of an acceleration time graph
07:45	? And you don't see jerk or drought ? You
07:46	might have to go of nothing because maybe a t
07:49	shirt didn't cover that topic because for most physics course
07:52	you won't see this . But in the event that
07:56	you do see those terms , that's what it is
08:01	. Now , what about the area of an acceleration
08:04	time graph ? By the way , the units for
08:06	this would be meters per second squared over seconds .
08:10	So it would be meters per second cube . So
08:14	that tells you dealing with the rate of change of
08:17	acceleration . Mhm . By the way the rate of
08:20	change of position is velocity . The rate of change
08:23	of velocity is acceleration and the rate of change of
08:26	acceleration as we just mentioned is jerk or job .
08:33	Now for the area we're multiplying why by X .
08:37	In this case acceleration by time . So what is
08:41	acceleration multiplied by time Acceleration has the units m for
08:47	a 2nd square . If we multiply that by seconds
08:50	we'll get the unit meters over seconds which represents the
08:54	unit for velocity . Yeah . So eight times T
08:59	. Gives you the change in velocity . If he
09:03	replaced Delta V with the final minus the initial you
09:08	get this familiar equation . V final is equal to
09:11	the initial plus 18 . Mhm . So the area
09:17	Mhm . Of an acceleration time graph is the change
09:22	in velocity . Now let's qualify that statement . I
09:28	think so let me changed its craft real quick .
09:35	So let's say we have a curve that looks like
09:37	this let's say that's our position time graph . And
09:45	let's put some numbers let's say this is one ,
09:47	This is three and this is five . Yeah .
09:54	Now if we draw the line at three , A
09:58	line that touches the curve at one point . Mhm
10:01	My lines are terrible . Let's do this one more
10:03	time . We'll make the best of that . But
10:05	a line that touches a curve at exactly one and
10:09	that line is known as the tangent line . The
10:13	slope of the tangent line gives you the instantaneous velocity
10:18	. If you're dealing with a position time graphs ,
10:20	let me say that one more time , the slope
10:23	of the tangent line of the position . Time graph
10:25	gives you instantaneous velocity . That is the velocity instantly
10:30	, once he is equal to three seconds . Now
10:34	let's say if we have two points at one and
10:37	size and let's draw a line connecting those two points
10:44	. A line that touches the curve at two points
10:48	. That line is a second line , The slope
10:50	of a second line gives you the average velocity .
10:54	The slope of the tangent line gives you instantaneous velocity
10:58	. To calculate the entertainers velocity . That's a little
11:00	difficult because it's hard to find the slope . At
11:02	one point . Now you could use calculus , you
11:05	could find the derivative and that can give you the
11:07	slope of the tangent line , which is the instantaneous
11:09	velocity . The slope of the secret line . You
11:13	could use algebra to get that answer . You could
11:16	use uh Y two over Y one divided by X
11:20	two minus X one . So it's easy to find
11:23	the slope of the second line which is the average
11:24	velocity . Now you can approximate the slope of the
11:28	tangent line using the slope of the second line .
11:31	So if we wanna get a good estimate of the
11:33	slope at exactly t equal stream . If we know
11:39	What the position is at let's say 2.9 and 3.1
11:44	. We can calculate the slope of the secret line
11:48	Of those two points 2.9 and 3.1 . To approximate
11:51	the slope of the tangent line at three . The
11:53	close to those two points gets a three the more
11:56	accurate the secret line becomes to the slope of the
11:59	tangent line . So as those two points get closer
12:03	and closer to three , the slope of the second
12:05	line approximates the slope of the tangent line . So
12:08	that's how you can find the slope of the tangent
12:10	line using this formula . Mhm . So if you
12:13	were to use values like 2.99 and three points or
12:16	one , it's going to be a very accurate estimate
12:19	of the slope of the tangent line . So let's
12:22	put this all together . When dealing with a position
12:24	time graph . The slope of the tangent line gives
12:27	you the instantaneous velocity . The slope of the secret
12:30	line gives you the average velocity when dealing with an
12:35	acceleration time graph . The area Does't give you the
12:39	instantaneous velocity nor does it give you the average velocity
12:42	, but it gives you the change in velocity .
12:45	That is the final -1 issue . So just make
12:48	sure you see that distinction and remember the slope of
12:53	a position time graph is velocity . The slope of
12:56	velocity . Time graph is acceleration . The slope of
13:00	an acceleration . Time graph is jerk or joke ,
13:02	which is not commonly used and the area of the
13:06	velocity time graph is displacement . The area of an
13:09	accelerated time graph is velocity . Those are things you
13:12	have to know if you want to answer questions with
13:14	these time graphs . Now , I'd like to make
13:18	a distinction between two similar time graphs , A position
13:27	time graph and a distance time graph in physics .
13:40	Position time graphs , you'll typically see them as X
13:43	versus T . For a distance time graph , you'll
13:46	see them as diversity . Now , what you need
13:50	to know is that velocity , which I just put
13:54	v velocity is displacement over time . Speed is equal
14:05	to the distance divided by the time . So here
14:11	we're dealing with division . So think of division as
14:14	slope . The slope of a position time graph is
14:18	velocity but the slope of a distance time graph is
14:26	speed . Because remember the slope is D over t
14:30	distance over time which is speed . So that's the
14:34	difference between a distance time graph and the position time
14:37	graph . The position time graph can give you velocity
14:41	if you calculate slope but a distance time graph ,
14:46	I mean as I said that correctly position time graph
14:48	can give you the velocity if you calculate the slope
14:51	but the distance time graph can give you the speed
14:54	. If you can't leave the slope . Remember velocity
14:56	is a vector and speed is a scale of quantity
15:01	velocity can be positive or negative but speed is always
15:04	positive . So make sure you see the difference between
15:07	the two . If you're dealing with a position time
15:09	graph versus a distance time graph . Now let's take
15:14	some more notes . So we said that velocity is
15:18	the rate of change of position . Therefore as the
15:22	position increases , the velocity is positive when a position
15:27	is a decrease in velocity is negative . So if
15:30	X is going up that means that the particle or
15:33	the object is moving to the right along the X
15:35	axis . If X is going down , that means
15:38	it's moving to the left . So any time velocity
15:41	is positive . When you're dealing with an ex varsity
15:44	graph , that means the particles moving to the right
15:47	. If losses negative it's moving to the left .
15:50	If the position is constant , that means the velocity
15:53	is zero . Now when the velocity is zero it
15:57	could be that the object is at rest or it
16:01	could be that the object is changing direction . So
16:09	it really depends on the shape of the graph .
16:11	So for instance let's say if you have a position
16:14	time graph that looks like this so notice that it's
16:19	horizontal for quite some time at that moment the particles
16:23	at rest but it could change instantly . Let's say
16:28	if it looks like this well let's do it like
16:37	this actually . So notice that it's horizontal for a
16:43	very brief moment . The tangent line Which is the
16:47	slope at at one The slope of the tangent line
16:52	is zero because the line is horizontal and so at
16:56	that instant it's at rest but it's changing direction .
17:01	So here the position is increasing . That means the
17:06	particles moving to the right because the slope is positive
17:10	, those velocities positive . Here is going down .
17:13	That means the slope is negative which means velocities negative
17:17	. So it's moving to the left . Yeah .
17:19	So it was moving to the right and now it's
17:21	moving to the left . So at the top at
17:23	that peak where the slope is zero it's at rest
17:27	for a very very short time . Or more specifically
17:30	it's changing direction going from right to left . So
17:35	when velocity is zero the particle could be at rest
17:39	or the particle could be a change in direction .
17:43	So keep that in mind . Now we said that
17:47	velocity is the rate of change of position , acceleration
17:52	is the rate of change of velocity . So whenever
17:56	the acceleration is positive , that means that the velocity
17:59	is increasing when the acceleration is negative , the velocity
18:04	is a decrease in . If the acceleration is zero
18:08	, that means that the velocity is constant . Now
18:13	speed is the absolute value of velocity . So if
18:18	the velocity is positive five m/s , that means that
18:22	the speed is positive five . If the velocity is
18:26	negative for meters per second , that means that the
18:29	speed is positive for meters per second . So if
18:33	a particle is moving to the left at four m
18:35	per second , you would say that the speed of
18:37	the particle is simply four m per second , speed
18:40	is always positive . Now we need to talk about
18:45	when an object is speeding up versus when it's slowing
18:47	down , how can you determine when it's speeding up
18:55	and when it's slowing down ? Here's a quick and
19:03	simple way to get the answer . A particle is
19:09	speeding up when the acceleration and velocity have the same
19:12	sign either they're both positive or both negative . In
19:19	this situation the velocity is increasing , it's becoming more
19:23	positive because the acceleration is positive here even though the
19:26	velocities negative , it's becoming more negative . And so
19:31	if you get a larger negative the speed which is
19:34	the absolute value of velocity , that's becoming more positive
19:38	. So in both cases it's speeding up when the
19:43	signs of acceleration and velocity are different Where one is
19:46	positive and the other is negative and that's when the
19:50	particle or the object is slowing down . Yeah .
19:54	Mhm . So let's think about this conceptually here ,
20:00	when the acceleration is positive , that means velocities increase
20:02	in velocity is becoming more positive which means speed has
20:06	become more positive , so speed is increasing . Yeah
20:10	, the acceleration here is negative and the velocity is
20:13	negative because the acceleration is negative , the velocity is
20:16	becoming more negative . To think of it has gone
20:18	from negative five to negative Aid . But speed being
20:22	the absolute value of velocity it's going from 5-8 .
20:25	So speed is increasing in that case . Now for
20:30	this situation the velocity is negative but the acceleration is
20:33	positive which means that the velocity is becoming less negative
20:37	. So to illustrate this , let's see if the
20:39	velocity was negative . five , acceleration is making it
20:43	less negative , more positive . So it would become
20:46	like negative too due to a positive acceleration . The
20:50	velocity is increasing when acceleration is positive So -2 is
20:55	higher than -5 on a number line . But if
20:57	you take the absolute value of it You can see
20:59	why the speed is decreasing . Going from 5-2 .
21:03	Ass is going down Now a quick illustration for the
21:08	last one where acceleration is negative but velocity is positive
21:13	, The velocity is becoming less positive . So let's
21:16	say if it was eight With a negative acceleration it
21:19	can go down to four . Speed being the absolute
21:23	value of velocity will be the same , going from
21:25	8-4 . So the speedily decreasing and us any time
21:31	an object is slowing down , the acceleration and velocity
21:35	have opposite signs when it's speeding up , The acceleration
21:39	and velocity have the same sign . So that's a
21:41	quick and simple way to determine if an object is
21:43	speeding up or if it's slowing down . Now Let's
21:47	focus on the three linear shapes of a position time
21:50	graph . Now these linear shapes exist for any graph
21:56	. So you can have a straight line going up
21:58	, you could have a straight line going in a
22:00	horizontal direction or straight line going down . Those are
22:03	the three linear shapes that you're gonna be dealing with
22:07	now , because these shapes are linear , the slope
22:11	is constant , and for a position time graph flossie
22:14	is a slope . So for these three situations velocity
22:21	is constant and when velocity is constant , what can
22:26	you say about acceleration ? Anytime velocity is constant ,
22:31	acceleration is zero , So the acceleration is zero For
22:35	each of these three position time graphs . Now ,
22:39	for the first one , the position is increasing any
22:42	time , the position is increased in the velocity is
22:45	positive for the second one , position is not increasing
22:49	its constant , so the velocity is zero , which
22:53	means it could be at rest or it may be
22:55	changing direction . But for this particular shape here it's
22:59	at rest , it's not changing direction , it's not
23:02	going up and then down . But when via zero
23:09	, if you don't have the graph , just know
23:10	that it could be at rest or it could be
23:12	changing direction here , the position is decreasing . Whenever
23:17	the position decreases , the velocity is negative . So
23:23	when dealing with a position time graph , if you
23:24	have these three shapes , just no acceleration is zero
23:28	. If it's going up velocities positive , if it's
23:31	going down velocity is negative . If it's horizontal velocity
23:35	is zero . So in this side it's moving to
23:37	the right , along the X axis here , it's
23:40	movement to the left and for this particular picture ,
23:44	Specifically this one , it's at rest . Now let's
23:47	consider the next four fundamental shapes that you'll see with
23:51	a time graph . So now we don't have the
23:54	three linear shapes that we did before , but we
23:56	have four parabolic shapes . So because the position time
24:03	graph is not linear , the velocity is not constant
24:06	. Therefore we have an acceleration . But before you
24:10	go into acceleration , let's talk about velocity . So
24:14	for the first one is the velocity positive or negative
24:19	? Well , the position is increasing because we're going
24:22	up along the y axis , so therefore velocity is
24:27	positive because the slope is positive here the position function
24:31	is decreasing , so therefore velocity is negative for this
24:39	particular shape , the position function is still decreasing because
24:43	we're going down . So velocity is negative as well
24:47	, but here we are increasing , so X is
24:50	going up . Therefore velocity is positive . So that's
24:55	the velocity for each of those four situations . Now
24:58	, what about acceleration in calculus ? If you've taken
25:03	it before this shape is concave down . This shape
25:13	is known as concave up when dealing with a position
25:22	time graph . If you have a concave down shape
25:26	, the acceleration is negative , so down for negative
25:30	and up for positive . So for now go ahead
25:34	and write that down . So notice that these two
25:38	combined former concave down shape . I put them like
25:41	that together . So you can easily tell that the
25:45	acceleration will be negative . These two shapes combine form
25:48	a concave up shape , this is the first half
25:51	of it , and that's the second half . Yeah
25:57	. Mhm . So for the first two shapes ,
26:00	acceleration is negative And for the last two acceleration is
26:08	positive . Now , let's look at this from another
26:12	perspective , we know that the slope tells us the
26:17	velocity , but the way that the slope changes tells
26:20	us the acceleration velocity is the rate of change of
26:26	position , but acceleration is the rate of change of
26:29	velocity . So if we analyze how to slow changes
26:32	, we can get an idea of the acceleration for
26:34	this graph . So at this point The slope appears
26:40	to be approximately one . Mhm . This is a
26:43	slope of one when it rises at a 45° angle
26:47	. When it's horizontal , the slope is zero .
26:49	If it goes down at a 45 degree angle ,
26:52	the slope is negative one . Yes . So at
26:58	this point The graph appears to be rising at a
27:01	45 degree angle . So the slope is approximately one
27:04	here , But then it becomes almost horizontal where the
27:08	slope is approximately zero . So the slope is going
27:12	from 1-0 even though the velocity is positive . Because
27:19	access increasing , we're going up , The slope is
27:22	decreasing , it's going from 1-0 . Therefore we can
27:25	see why the acceleration is negative . Remember the slope
27:29	represents the velocity . So it's a velocity is going
27:32	from 1-0 . It's decelerating . That's why we can
27:36	say the acceleration is negative . So now let's analyze
27:40	the slope for the 2nd 1 . So here it
27:43	appears horizontal And at this point it looks like it's
27:46	going down at a 45° angle . So the slope
27:50	or the velocity is going from 0 to -1 .
27:54	So it's still decreasing , negative one is less than
27:57	zero . So we could see why the acceleration is
28:00	negative . Let me keep these numbers here . Now
28:10	, at this point the slope appears to be negative
28:12	one . It's going down at a 45 degree angle
28:15	, but it's becoming horizontal where the slope is zero
28:18	. So going from negative 1-0 , the slope or
28:21	the velocities increase in . Thus we can see why
28:24	the acceleration is positive and here it's clear to the
28:28	slope appears to be zero and here it's going to
28:30	one . So from 0 to 1 , the velocity
28:34	is increasing , which means the acceleration is positive .
28:39	So any time the acceleration is negative , the velocity
28:42	is decreasing when the acceleration is positive , the velocity
28:48	and the slope is increasing . Yeah . Now the
28:51	last thing that we need to talk about is if
28:54	it's speeding up or slowing down , it's looking at
28:57	the first graph on the left , would you say
28:58	it's speeding up or slowing down ? So if we
29:02	look at the signs for velocity and acceleration , they're
29:06	different . So we can say that it is slowing
29:11	down . Remember speed is the absolute value of velocity
29:16	. If you go from 1-0 , you're slowing down
29:20	here , the signs are the same . So it's
29:24	going to be speeding up this time , velocity is
29:27	zero . Speed being the absolute value of velocity is
29:31	not negative one but positive one . So in this
29:34	case the speed is going from zero , it's a
29:36	plus one . It's speeding up Here , the speed
29:39	is going from 1-0 . So we can see why
29:42	it's slowing down now . For the next case the
29:49	signs are opposite , so therefore it's going to be
29:52	slowing down . Yeah , So if velocity is negative
29:56	one speed is positive one . So going from 1-0
29:59	, we could see why it's slowing down . And
30:03	for the last case both velocity and acceleration have the
30:07	same sign , so it's going to be speeding up
30:13	These numbers , none of them are negative , so
30:15	speed is gonna be the same , it's gonna be
30:17	0-1 . And so in that case it's speeding up
30:20	as well . So now you can answer almost every
30:24	question when dealing with position time graphs , you know
30:28	how to determine if the velocity is positive or negative
30:31	if it's increasing or decreasing . Thus , you know
30:33	how to determine the sign of acceleration and whether if
30:36	it's speeding up or slowing down .

Summarizer

DESCRIPTION:

This physics video tutorial provides a basic introduction into motion graphs such as position time graphs, velocity time graphs, and acceleration time graphs. It explains how to use area and slope to calculate the velocity, acceleration, displacement, and whether if the particle is speeding up or slowing down. It also explains how to determine if the velocity is increasing or if the acceleration is positive.

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Velocity Time Graphs, Acceleration & Position Time Graphs - Physics is a free educational video by The Organic Chemistry Tutor.

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