Shadowing Practice: Proportional reasoning with motion | AP Physics | Khan Academy - Learn English Speaking with Video
Elige un modo de práctica
Cada modo abre una sala de práctica a pantalla completa.
210 oraciones
Si las oraciones son demasiado cortas o largas, haz clic en Editar para ajustarlas.
1
NASA is researching how to send humans to Mars by as early as 2030.
2
Now, this is a complex mission because you're traveling for millions of kilometers, and this will involve a lot of things like when you think about how much fuel you need,
3
how much oxygen we need, and then how much time we'll be spending over there, and how much radiation exposure humans will be having.
4
So many different things.
5
So how do we figure out what's the best approach?
6
Well, what we usually do is try to come up with different plans.
7
I can call it as mission A, mission B, mission C, and so on and so forth.
8
And then we try to create mathematical models for them and then compare the models to find the trade-offs.
9
And then eventually we finalize on one of them.
10
And so the goal of this video is to get a glimpse of how to create mathematical models and compare them.
11
Now, of course, we'll not do it for such a complex mission.
12
We'll simplify it.
13
So in our case, we'll assume that the spacecraft is traveling in a straight line because that's simple.
14
and we'll assume that it's traveling with a constant acceleration.
15
And lastly, we'll assume that the initial velocity is zero.
16
So for the first case, let's assume, let's call this mission A, let's assume that the acceleration is 10 meters per second squared,
17
which is very close to the acceleration due to gravity on Earth.
18
So the astronauts over there would be feeling pretty much at home.
19
And the spacecraft will travel some distance, let's call it delta X, in some time.
20
But now let's create a second plan, second mission.
21
in which, again, it's constant acceleration, initial velocity is zero, it's going to travel the same delta x, but in half the time.
22
Okay?
23
Now, our goal is to compare some of the mission parameters.
24
The first thing we could compare is the average velocity.
25
I mean, think about it, right?
26
If we want to go from here to here in half the time as over here, then clearly the average velocity over here would be higher than over here.
27
That makes intuitive sense.
28
But how much higher?
29
We want to compare that.
30
So to do that, we want to build a mathematical model for the average velocity and then compare them.
31
So let's do that.
32
We can try using the model for average velocity, which is delta x divided by t.
33
Let's see if this model is useful for us.
34
Well, first of all, we need to compare average velocity.
35
So it's good that that's there.
36
Okay, what about delta x?
37
We know the relationship between them.
38
They're exactly the same.
39
Delta x for mission B is the same as delta x for mission A.
40
We're considering the same delta x value.
41
So that's good.
42
And what about time?
43
We also know the relationship between them.
44
We know the time over here has to be half the time over here.
45
So time for B is half the time for A.
46
So since we know the relationship for this between these two and the relationship for this between these two, we can now use this equation,
47
use this model, to find the relationship between the average velocity between the two.
48
So this is going to be a useful model.
49
Now imagine if we had used a model for average velocity which involved acceleration.
50
Then that wouldn't be useful because we don't know the relationship between the accelerations.
51
Right?
52
We don't know what the acceleration over here is.
53
And so that's why it's important to pick the right models.
54
But we don't have to worry too much.
55
If you do pick a wrong model, we'll figure it out and we'll scratch it and we'll use another model.
56
Trial and error.
57
No big deal.
58
Okay?
59
Anyways, let's go ahead with this.
60
Let's write down the average velocity for mission B.
61
So we could say the average velocity for mission B would be delta x B divided by T B.
62
And the average velocity for mission A would be delta x A divided by T A.
63
We know delta x B and delta x A are the same.
64
It's just delta x.
65
So let's just call them as delta x.
66
And now to compare them, we can just divide the two equations.
67
And now we simplify.
68
The delta x divides out.
69
And so you get that equals 1 over Tb divided by 1 over Ta, which is Ta divided by Tb.
70
And now we know what Tb is.
71
The time for this is half the time for A.
72
We can plug that in.
73
So if you get half Ta, the Ta divides out and you end up with 2.
74
So look, this ratio ends up becoming 2.
75
So we can rearrange now and write
76
that the average velocity in mission B will be twice as much as the average velocity in mission a.
77
So to cover the same delta x in half the time, we need twice the average velocity, which is not super obvious because we're dealing with accelerated motion over here.
78
But now the interesting question is, could we have just looked at this equation without doing the math, figure this out?
79
And the answer is yes.
80
If you look at this model carefully, because delta x is the same for both, we can look at this and we can say, hey, average velocity is proportional to 1 over t,
81
or it's inversely proportional to t.
82
What this means is that if t changes by some factor, your average velocity will change by the reciprocal of that factor.
83
So if t becomes double, your average velocity will be reciprocal of that, half.
84
If t triples, the average velocity will be reciprocal of that, one by third.
85
In our case, the t became half, so the average velocity would be reciprocal of half, which is two.
86
And so immediately, just by looking at this, we could have said, hey, if the t becomes half, the average velocity would double.
87
Powerful, right?
88
All right, now let's see if we can compare something else.
89
Let's compare their accelerations.
90
What's the acceleration in mission B compared to mission A?
91
And again, for that, we need to use a model, this time a mathematical model that involves acceleration.
92
And one of such models is this.
93
This is the model for things that are moving with constant acceleration, right?
94
Again, let's look at stuff that we already know and then see if this is going to be useful for us.
95
So what do we know?
96
Well, first of all, since we have x0, which is the initial position, which is over here, we can just set that to 0.
97
And then the x, which is the final position, we can just call that as delta x.
98
So we know those two.
99
That's the same for both of them.
100
We also know the initial velocity, which is v0.
101
That is 0.
102
And we know the time over here needs to be half the time over there.
103
and finally we know the acceleration of the first one
104
so these are the things that are given to us
105
so the first thing we can do is plug in whatever zeros are to make our model slightly simpler
106
so if you do that this goes to zero this becomes delta x this goes to zero
107
so you'll get delta x equals half a t squared
108
and since i want to compare accelerations i will rearrange this to get the acceleration
109
so acceleration becomes two delta x divided by t squared and again let's see if this model is useful for us.
110
I want to compare acceleration, so that's great.
111
I need accelerations.
112
Do I know the relationship between delta x?
113
Yes, they are the same.
114
And do I know the relationship between time?
115
Yes, I do.
116
So I can use this to find the relationship between the accelerations.
117
It'll be a great idea to pause the video and see if you can try this on your own, very similar to what we did earlier.
118
All right, let's do this.
119
So we can write down the accelerations for both the missions.
120
So for b will be 2 times delta x b by db squared, and for a will be 2 delta x a by ta squared.
121
But we know delta x b and delta x a are exactly the same, so we can just get rid of a and b over there.
122
And we can divide the two, just like before, and then simplify.
123
So the 2 delta x and 2 delta x can divide out, leaving us with 1 over tb squared divided by 1 over T A squared.
124
And then we can rearrange this to get T A squared divided by T B squared.
125
And again, we can finally plug in what T B is.
126
T B is half T A.
127
If we plug that in over here, we get half T A, the whole squared.
128
Finally, T A squared divides out, leaving us with 1 divided by 1 over 4, which is 4.
129
So from this, I now know that the acceleration in mission B would be four times as the acceleration in mission A.
130
And so there we have it.
131
We need four times more acceleration here compared to over here.
132
Four times more is four times 10, that is 40.
133
And then we could say that, hey, 40 meters per second square is too much of an acceleration for humans to withstand.
134
That's not gonna be possible because we'll be traveling for a long time.
135
And so we could say that, no, we can't do that.
136
Even if we reach in half the time, that's not possible.
137
But anyways, just like before, could we have figured this out without doing the whole math?
138
and the answer is again yes again
139
if you look at the model carefully we see
140
that delta x is the same for both of them
141
which means acceleration will be proportional to one over t squared
142
or inversely proportional to t squared this means whatever factor t
143
changes by acceleration will change by the reciprocal of the square
144
so if t were to double acceleration would be the reciprocal half square, one fourth.
145
If t were to triple, acceleration would change by one over three, reciprocal square, one ninth.
146
But in our case, t became half.
147
So acceleration would be reciprocal two squared, four.
148
And there you have it.
149
This is a very powerful way of doing this.
150
Since we're having so much fun over here, we should try one more plan, mission C.
151
Here, we'll keep the same acceleration as before, but we'll allow the spacecraft to travel for 50% more time than before.
152
So same acceleration, but 50% more time, it's going to travel farther, right?
153
Now the question is how much farther?
154
So we know what to do by now.
155
Think about a mathematical model.
156
So again, since we're dealing with positions and accelerations, let's use the same model as before.
157
Write down what we know.
158
And at any moment, feel free to pause and try this on your own, okay?
159
But let's write down what we already know.
160
We know, I mean, we can set our x to be 0, the initial position to be 0, and the final position would just be x.
161
So we can just set x0 to be 0.
162
We also know the v0 initial velocity is 0.
163
So we know that.
164
We also know the accelerations are the same in this time.
165
So acceleration case A and case C is the same.
166
And we are allowing for 50% more time.
167
So we know that the time here is 50% more compared to time A, which means 1.5 times A.
168
So Tc must be 1.5 times T A.
169
And again, we can plug in zeros to simplify.
170
So this goes to 0, this goes to 0 and that gives us a simplified model x
171
which is the final position which we want that is the model
172
so let's see if it's useful okay we want x we want to compare that
173
so it's good that's there do we know the relationship between
174
the accelerations yes the same accelerations do we know the relationship between the time yes we do
175
so we know the relationship between time 1.5 times ta and
176
so we can figure this out again we can do the math
177
but we also know how to do this in a shortcut now, right?
178
So we can look at this model and we can say that, hey, since the acceleration is the same, since A is the same,
179
x is directly proportional to t squared.
180
So now whatever factor t changes by, x will change by the square of that factor.
181
You can see that's directly proportional this time, right?
182
So if t doubles, x will be, x will change by a factor of two squared.
183
If t triples, x will change by a factor of 3 squared.
184
In our case, t has become 1.5 times more.
185
So x will change by a factor of 1.5 squared.
186
So we can immediately write xc, the final position over here, okay?
187
That has to be 1.5 times square xa, the final position over here.
188
And if you simplify, 1.5 square is 2.25.
189
And so we immediately get the answer.
190
So xc would be 2.25 times xa, which is amazing if you think about it, right?
191
Just by 50% more time, you're allowing, it'll travel more than twice the distance compared to the first one.
192
And by the way, we can check the math and I'll not go through all the steps over here.
193
I'll just show you all the steps.
194
You can pause the video and you can just see.
195
If you divide it and do it the long way, you get the same answer.
196
But anyways, look at what this means.
197
This means that, you know, in the first case, if we allowed it to travel for one year
198
and let's say the distance it traveled was a billion kilometers.
199
In the second case, if we allow it 50% more time, which is one and a half years, it will travel 2.25 billion kilometers.
200
That's awesome.
201
So long story short, by using mathematical models, we can see how changing one variable affects the other variable.
202
This is super useful in comparing scenarios.
203
What's important is that you don't need actual values.
204
You just need the models and you can divide them out and you can figure out and you can compare, you know, whatever you want to compare.
205
And another way is you can do it without dividing.
206
We can do it without doing the math by just looking at the model, seeing what variables are the same for the both,
207
and then figuring out the proportionality relationship, the right proportionality relationship.
208
If you know the factor by which one variable changes, we can figure out the factor by which the other variable would change as well.
209
This is not just useful for kinematics.
210
It's useful for all physics.
Descargar app
Todo lo que necesitas para hablar con fluidez
Pronunciación con IAEvalúa cada oración
Práctica de IPADomina cada sonido
VocabularioConstruye tu banco de palabras
Juego de vocabularioAprende mientras juegas
Mismo canal
B16
LearnStorm Growth Mindset: How to write a SMART goal
American AccentBusiness EnglishHigh School StudentsUniversity Students
C115
Introduction to high school physics | Khan Academy
American AccentHigh School StudentsUniversity Students
B19
States of matter | Middle school chemistry | Khan Academy
American AccentTOEFL PrepCambridge Exam PrepHigh School Students
B12
Elements | Middle school chemistry | Khan Academy
American AccentHigh School StudentsUniversity Students
B12
Newton's second law | Middle school physics | Khan Academy
American AccentHigh School StudentsUniversity Students
C13
Derivative as slope of a tangent line | Taking derivatives | Differential Calculus | Khan Academy
American AccentCambridge Exam PrepUniversity StudentsWorking Adults
C15
Molecules, crystals, and diatomic elements | Middle school chemistry | Khan Academy
American AccentHigh School StudentsUniversity Students
B13
Atoms | Middle school chemistry | Khan Academy
American AccentTOEFL PrepCambridge Exam PrepHigh School Students
C13
Pixar in a Box | Welcome to Pixar in a Box | Khan Academy
American AccentHigh School StudentsUniversity Students
C12
Biology overview
American AccentUniversity Students
C12
Newton, Leibniz, and Usain Bolt | Derivatives introduction | AP Calculus AB | Khan Academy
American AccentCambridge Exam PrepUniversity StudentsWorking Adults
B12
Introduction to interest | Interest and debt | Finance & Capital Markets | Khan Academy
American AccentBusiness EnglishUniversity StudentsWorking Adults
B2How to rationalize a denominator | Exponent expressions and equations | Algebra I | Khan Academy
Daily ConversationHigh School Students
FOR YOU
Recomendar Video
C12
97 oraciones
Vectors | Chapter 1, Essence of linear algebra
American AccentBusiness EnglishUniversity StudentsWorking Adults
C12
224 oraciones
20% Speed of Light!! NEW Light Engine is INSANE!
Daily ConversationUniversity StudentsWorking Adults
C11
134 oraciones
Passage Planning: The Four Stages of Voyage Planning Explained
Business EnglishWorking Adults
C118
160 oraciones
Stop Walking 10,000 Steps/Day (do this for 10 minutes instead)
Business EnglishUniversity StudentsWorking Adults
B23
265 oraciones
Learn English with the NEWS 🌐 Advanced Vocabulary and Shadowing Practice for Fluency
American AccentIELTS PrepTOEFL PrepBusiness English
C12
32 oraciones
Equilibrium of Rigid Bodies (2D - Coplanar Forces) | Mechanics Statics | (Solved examples)
Business EnglishUniversity StudentsWorking Adults
B21
46 oraciones
Automatic Bullseye, MOVING Dartboard
American AccentBusiness EnglishUniversity StudentsWorking Adults
C15
58 oraciones
How to Make a Kurzgesagt Video in 1200 Hours
Business EnglishUniversity StudentsWorking Adults
C12
15 oraciones
Particle Motion in Matter
University StudentsWorking Adults
C14
82 oraciones
Elon's SpaceX Tour - Falcon 1, Falcon 9 and Dragon
Business EnglishUniversity StudentsWorking Adults
Vocabulario y notas de pronunciación para esta lección
Esta lección de conversación de nivel C1 se basa en el vídeo “Proportional reasoning with motion”. Las palabras que más se repiten: acceleration, delta, model, velocity, mission. Este vídeo tiene 210 frases y 2506 palabras para practicar shadowing. La parte hablada dura 12:45. El hablante habla rápido, unas 196 palabras por minuto, así que espera sonidos enlazados y reducidos. El 83 % de las palabras está entre las 3.000 más comunes del inglés; conviene repasar el resto antes de empezar.
Vocabulario clave de este vídeo
Las 15 palabras más avanzadas del vídeo, con su pronunciación y significado:
| Palabra | Pronunciación | Significado |
|---|---|---|
| acceleration sustantivo | /əkˌsɛl.əˈɹeɪ.ʃən/ | aceleración, aceleramiento |
| velocity sustantivo | /vəˈlɑsəti/ | velocidad |
| reciprocal adjetivo | /ɹɪˈsɪpɹək(ə)l/ | mutuo, recíproco |
| simplify verbo | /ˈsɪmplɪfaɪ/ | simplificar |
| proportional adjetivo | proporcional, alícuota | |
| mathematical adjetivo | /ˌmæθ(.ə)ˈmæt.ɪ.kəl/ | matemático |
| rearrange verbo | /ˌɹiːəˈɹeɪndʒ/ | reacomodar, reacotejar |
| spacecraft sustantivo | /ˈspeɪsˌkɹæft/ | nave espacial |
| pause sustantivo | /pɔːz/ | pausa |
| equation sustantivo | /ɪˈkweɪ.ʒən/ | ecuación |
| inversely adverbio | inversamente | |
| proportionality sustantivo | /pɹəpɔɹʃəˈnæləti/ | proporcionalidad |
| meter sustantivo | /ˈmitəɹ/ | medidor, contador |
| finalize verbo | /ˈfaɪ.nə.laɪz/ | finalizar |
| kinematics sustantivo | /ˌkɪnəˈmætɪks/ | cinemática, cinema |
Phrasal verbs que vas a escuchar
| Palabra | Significado |
|---|---|
| figure out verbo | averiguar, captar |
| write down verbo | apuntar, anotar |
| come up with verbo | ingeniar, ingeniarse |
| end up verbo | terminar, ir a parar |
| go through verbo | atravesar |
| step over sustantivo | bicicleta |
Frases que vale la pena repetir
Frases cortas y completas del vídeo que puedes reutilizar en la conversación diaria:
- Let's see if this model is useful for us.
- We're considering the same delta x value.
- We don't know what the acceleration over here is.
- Anyways, let's go ahead with this.
- Do I know the relationship between delta x?
Gramática en este vídeo
Las estructuras que más usa el hablante, con las palabras exactas del vídeo:
| Estructura | En el vídeo |
|---|---|
| Oraciones condicionales if + oración, will/would + verbo — una condición y su resultado | If t triples, the average velocity will be · if t were to double acceleration would be · If t were to triple, acceleration would change |
| Oraciones de relativo who / which + oración — información extra sobre una persona o cosa | velocity, which is · half, which is · position, which is |
| Present perfect have/has + participio pasado — una acción pasada que sigue importando ahora | have just looked · have figured · has become |
Pronunciación a tener en cuenta
El hablante usa 31 contracciones y formas reducidas, como we'll, don't, we're. Dilas en su forma corta, tal como las oyes.
- Los sonidos de “th”: mathematical /ˌmæθ(.ə)ˈmæt.ɪ.kəl/, withstand /wɪðˈstænd/, ninth /naɪnθ/
- Los sonidos de “sh” y “zh”: acceleration /əkˌsɛl.əˈɹeɪ.ʃən/, equation /ɪˈkweɪ.ʒən/, proportionality /pɹəpɔɹʃəˈnæləti/, shortcut /ˈʃɔːtkʌt/
- Palabras largas — cuida el acento: acceleration /əkˌsɛl.əˈɹeɪ.ʃən/, velocity /vəˈlɑsəti/, reciprocal /ɹɪˈsɪpɹək(ə)l/, mathematical /ˌmæθ(.ə)ˈmæt.ɪ.kəl/, proportionality /pɹəpɔɹʃəˈnæləti/
Sonidos difíciles para hispanohablantes:
- /v/ — no es /b/: los dientes tocan el labio inferior: velocity /vəˈlɑsəti/, intuitive /ɪnˈtjuːɪtɪv/
- /z/ — sonora, no /s/: pause /pɔːz/, anyways /ˈɛn.iˌweɪz/, finalize /ˈfaɪ.nə.laɪz/
Cómo practicar con este vídeo
- Escucha el vídeo entero una vez sin hablar y anota las palabras que no conoces.
- Empieza a velocidad 0,75×, haz shadowing frase por frase y vuelve a la velocidad normal cuando te resulte fácil.
- Grábate y compara con el original, prestando atención a palabras como acceleration, velocity, reciprocal.
¿Qué es la Técnica de Shadowing?
Shadowing es una técnica de aprendizaje de idiomas respaldada por la ciencia, desarrollada originalmente para la formación de intérpretes profesionales y popularizada por el políglota Dr. Alexander Arguelles. El método es simple pero poderoso: escuchas audio en inglés nativo y lo repites en voz alta de inmediato, como una sombra que sigue al hablante con solo 1-2 segundos de retraso. A diferencia de la escucha pasiva o los ejercicios de gramática, el shadowing obliga a tu cerebro y músculos de la boca a procesar y reproducir simultáneamente patrones de habla reales. Las investigaciones muestran que mejora significativamente la precisión de la pronunciación, la entonación, el ritmo, el habla conectada, la comprensión auditiva y la fluidez al hablar, convirtiéndola en una de las metodologías más efectivas para la preparación del IELTS Speaking y la comunicación en inglés en el mundo real.