Shadowing Practice: Derivatives: Crash Course Physics #2 - Learn English Speaking with Video
בחר מצב תרגול
כל מצב פותח חדר תרגול במסך מלא.
138 משפטים
אם המשפטים קצרים או ארוכים מדי, לחץ על ערוך כדי להתאים אותם.
1
Every discipline of science has its very own special language, the way it communicates the ideas that it investigates.
2
For example, biology finds order in the world by giving every living thing a name in Latin.
3
Chemistry has a system of prefixes, suffixes, and numerals to tell you, in a word or two, the exact composition of an atom or a compound.
4
Physics has to communicate its ideas differently.
5
The language of physics is mathematics.
6
Because if you're trying to describe how the world works, you really have to know how things relate to each other in a mathematical way.
7
For example, we've been talking a lot about position, velocity, and acceleration, and how they're all connected.
8
Velocity is a measure of your change in position, and acceleration is a measure of your change in velocity.
9
They're connected.
10
One quality will describe how the other is changing.
11
And the way we describe change in mathematics is through calculus.
12
Calculus explains how and why things change using derivatives, which help you to determine how an equation is changing.
13
as well as with integrals, which you can use to calculate the area under a curve.
14
Derivatives and integrals themselves are closely connected, but let's start with derivatives.
15
You probably won't be able to go straight from this lesson to your calculus final, but hopefully in about 10 minutes you will be able to understand some of the maths
16
that scientists have been using to think about physics for the last 400 years or so.
17
And you'll also have a new way to fight speeding tickets.
18
You know, just in case.
19
Last time we talked about that unfortunate incident where you got a speeding ticket.
20
Your speedometer was broken, but because we knew your acceleration, we were able to calculate how fast you were going when the cops pulled you over.
21
So now, let's talk about what happens next.
22
Say the police drive off.
23
You're ready to get back on the road, so you hit the gas and zoom forward, moving faster and faster.
24
But in this scenario, we don't know your acceleration we only know how much your position is changing over time.
25
In this instance, your position happens to be equal to the amount of time you've been driving squared.
26
So we'd write that as the equation x equals t squared.
27
20 seconds in, you pass a detector with a sign that tells you your speed.
28
You keep driving, foot still on the gas, before you realize what number you saw on the sign.
29
And oh no!
30
You just got a speeding ticket in the last episode for
31
doing 126 km an hour in a 100 km an hour zone.
32
And now the detector says you're going even faster!
33
Now, you want to know if the number on the detector is accurate.
34
In other words, you want to find your velocity at the exact moment you passed it.
35
That velocity is just a measure of your changing position, its derivative.
36
So to find your velocity, we'll need to find the derivative of your position.
37
And in order to determine that, we first need to talk about limits.
38
Not speed limits, I mean the derivatives kind.
39
I'll explain.
40
Limits are based on the idea that if you have an equation on a graph, you can often predict what it's going to look like at one point, just by knowing what it looks like at the surrounding points.
41
For example, let's say you have a graph of x equals t squared from our speeding scenario above,
42
and you want to find out how your position is changing at the exact moment that time is equal to zero.
43
That is what we call the limit as t approaches zero.
44
So you take a look around at what's happening around t equals zero.
45
At t equals one, x is one.
46
At t equals zero point five, x is zero point two five.
47
And at t equals 0.1, x is 0.01.
48
You can probably tell that as we get closer and closer to t equals zero, your value of x is getting closer to zero, too.
49
That's what mathematicians mean when they talk about a limit.
50
Limits are useful because they can help predict what happens as you make intervals smaller.
51
An interval is just a range on a graph.
52
It's the space between two points on the horizontal axis.
53
So the first thing we can try is calculating your average velocity over the interval from 15 to 20 seconds.
54
To do that, we use an equation that we talked about last time – your average velocity, which is equal to the change in your position divided by the change in time.
55
That turns out to be 35 meters per second.
56
Problem is, it's just an average.
57
It's not exactly how fast you were going after 20 seconds of acceleration when you passed the detector.
58
Because of limits, we know
59
that you could get a little closer to the right number by calculating your average over smaller and smaller intervals.
60
Then you'd see that the number seems to be getting closer and closer to 40 meters per second.
61
Which means you're going to need to slow way down
62
if you don't want to get your second speeding ticket of the day.
63
But that's the idea of derivatives.
64
You can use infinitely tiny intervals to figure out exactly how an equation is changing at any moment.
65
You can even come up with an equation to describe the change.
66
That's exactly what velocity is, an equation that describes change in position.
67
An acceleration describes change in velocity.
68
So we call velocity the derivative of position, and acceleration the derivative of velocity.
69
Now, when it comes to how you can express a derivative in writing, mathematicians have come up with shortcuts.
70
Like what's known as the power rule.
71
As the name suggests, it's used for equations with variables raised to powers or exponents, as long as the exponent is a number.
72
For example, x equals t squared would work with the power rule, because t is raised to the power of 2.
73
The power rule says that, for these kinds of equations, to calculate the derivative, all you need is one weird trick.
74
Take the number of that exponent, in this case 2, and stick it in front of the variable.
75
Then you subtract 1 from the exponent.
76
And that's your derivative!
77
So the derivative of x equals t squared is just 2t, Which means that no matter how many seconds you've got your foot on the gas, your velocity will be 2t.
78
So double the number of seconds.
79
After 5 seconds, you were going a modest 10 meters per second.
80
But after 20 seconds, you were going a full 40 meters per second, which is not good.
81
We'd write that like this, where dx over dt is just a way of saying
82
that we're taking the derivative of the part of the equation that involves t.
83
Or, as a mathematician would put it, we're taking the derivative of x with respect to t.
84
You'll also sometimes see this written in a different way.
85
If f is equal to t squared, then f prime of t is equal to 2t.
86
Now let's try to find a couple more derivatives using the power rule.
87
X equals 7t to the power 6 is another power-style equation.
88
It has a variable t raised to the power 6, with a number in front of it, 7.
89
The first thing we do is take the exponent and stick it in front of the variable.
90
But there's already a number in front of t, 7.
91
So we end up multiplying them.
92
7 times 6 is 42.
93
Then we subtract 1 from the power that t is raised to.
94
So we end up with 42t to the power 5.
95
Same goes for equations where the exponents are fractions or decimals.
96
So the derivative of t to the power half is half t to the negative one-half.
97
It works for negative exponents, too.
98
The derivative of t to the power minus 2 is just negative 2t to the negative third.
99
Now, there are a few more equations whose derivatives you should understand.
100
Trigonometry, which we use to calculate the angles and size of triangles, is going to This is going to come up a lot in physics, because we'll be using right-angled triangles all the time.
101
So it's a good idea to know how to find the derivatives of sine x and cosine x.
102
Sine tells you that if you have a right-angled triangle, and x is the angle in that triangle, then sine x will be the length of the side opposite that angle, divided by the hypotenuse.
103
Cosine does the same thing, just with the side next to the angle, divided by the hypotenuse.
104
So their graphs will tell you what those ratios will be, depending on the angle.
105
We can actually try to guess the derivative of sine x, just by looking at its graph.
106
We can see that the curve has turning points every so often, at x equals minus 90 degrees, x equals 90 degrees, and so on, repeating every 180 degrees.
107
Meaning at those points, the equations aren't changing at all.
108
So the derivative at these turning points is also going to be exactly zero.
109
Let's pull up another graph where we'll plot the derivative and put little dots where we'll know it'll be zero.
110
Now, what's happening between those turning points?
111
Well, from minus 270 to minus 90 degrees, sine x is decreasing.
112
In other words, its change, and therefore its derivative, must be negative.
113
Then, from minus 90 to 90 degrees, sine x is increasing, so it'll have a positive derivative, and so on.
114
There are actually a lot more clues in this graph to help us find the derivative, but we already know enough to make a decent guess.
115
If we smoothly connect the dots on the graph of our derivative, keeping in mind where the curve should be positive and where it should be negative,
116
hey, this derivative is looking a whole lot like the graph of cosine x.
117
That's because it is!
118
The derivative of sine is just cosine, and that's going to come up a lot.
119
And so will these, which you can work out on your own by repeating what we just did with the graphs of sine x
120
and cosine x.
121
Another important derivative that comes up a lot is a very special case, and that's e to the x.
122
The derivative of e x is just...e x.
123
Yep, and that's it, no matter what.
124
In fact, that's one way to define e, which is kind of like pi, in the sense that it's a simple letter, representing a very specific, irrational number,
125
about 2.718, with more digits after the decimal point that go on forever.
126
It has all sorts of uses in calculus, but it also shows up when you're studying things like finance and probability.
127
Armed with all these ways to find derivatives, you could pretty much take any equation of your position and calculate its derivative, and therefore, your velocity.
128
In the same way, you could take the derivative of your velocity and find your acceleration.
129
But there's a whole other part of calculus that we haven't even talked about yet.
130
Integrals, which will let you do this backwards.
131
With integrals, you can use your acceleration to find your velocity, and your velocity to find your position.
132
But we'll save that for next time.
133
Today you learned about limits and that derivatives use them to describe how an equation is changing.
134
We also talked about a few different kinds of derivatives – powers, constants, trigonometry, and e to the power x.
135
Crash Course Physics is produced in association with PBS Digital Studios.
136
You can head over to their channel to check out amazing shows like Deep Look, The Good Stuff, and PBS Space Time.
137
This episode of Crash Course is filmed in the Dr. Cheryl C.
138
Kinney Crash Course Studio, the help of these amazing people and our graphics team is Thought Cafe.
הורד אפליקציה
כל מה שאתה צריך כדי לדבר בשטף
הגיית AIציון לכל משפט
תרגול IPAשלוט בכל צליל
אוצר מיליםבנה את מאגר המילים שלך
משחק אוצר מיליםלמד תוך כדי משחק
אותו ערוץ
B21
The Bicameral Congress: Crash Course Government and Politics #2
Daily ConversationHigh School StudentsUniversity Students
B21
Crash Course US History Preview
Daily ConversationUniversity Students
C1What's all the Yellen About? Monetary Policy and the Federal Reserve: Crash Course Economics #10
Daily ConversationUniversity Students
C12
How Water Shapes the Land: Crash Course Geology #9
Daily ConversationUniversity Students
B24
How Often do Asteroids Hit the Earth?: Crash Course Geology #20
Daily ConversationHigh School StudentsUniversity Students
B210
Crash Course Sex Ed Preview
Daily ConversationUniversity StudentsWorking Adults
C13
Indus Valley Civilization: Crash Course World History #2
Daily ConversationUniversity Students
B22
Ancient Egypt: Crash Course World History #4
Daily ConversationHigh School StudentsUniversity Students
C12
What is Engineering?: Crash Course Engineering #1
Business EnglishUniversity StudentsWorking Adults
B22
The Persians & Greeks: Crash Course World History #5
Cambridge Exam PrepHigh School StudentsUniversity Students
C13
The Secret to Business Writing: Crash Course Business - Soft Skills #3
Business EnglishUniversity StudentsWorking Adults
C12
Supervised Learning: Crash Course AI #2
Business EnglishUniversity StudentsWorking Adults
C1Why Are US Politics Today So Divisive?: Crash Course US Government #1
Daily ConversationUniversity Students
C13
The Periodic Table: Crash Course Chemistry #4
IELTS PrepTOEFL PrepCambridge Exam Prep
B22
Where Do Diamonds Come From?: Crash Course Geology #8
IELTS PrepTOEFL PrepCambridge Exam Prep
C11
Tissues, Part 1: Crash Course Anatomy & Physiology #2
Cambridge Exam PrepUniversity StudentsWorking Adults
C13
Where Did Democracy Come From, and Does It Still Work?
IELTS PrepTOEFL PrepUniversity Students
C12
The Nucleus: Crash Course Chemistry #1
IELTS PrepTOEFL PrepUniversity Students
B21
Defense Against the Dark Arts of Influence: Crash Course Business Soft Skills #2
Business EnglishUniversity StudentsWorking Adults
B24
Planning & Organization: Crash Course Study Skills #4
Business EnglishHigh School StudentsUniversity Students
FOR YOU
המלץ על סרטון
C13
119 משפטים
Mathematics and Physics | Lesson 2 | Understanding the Connection
Daily ConversationUniversity Students
C13
147 משפטים
We Traveled Back in Time. Now Physicists Are Angry.
Daily ConversationUniversity StudentsWorking Adults
C1287 משפטים
Differential equations, a tourist's guide | DE1
Daily ConversationUniversity Students
C11
498 משפטים
Give me 31 minutes, I will make PyTorch click forever
Daily ConversationUniversity Students
C18
156 משפטים
How Quantum Batteries Break Every Rule of Charging
Daily ConversationUniversity StudentsWorking Adults
C13
81 משפטים
Everything You Need to Know About DNS: Crash Course System Design #4
Daily ConversationUniversity StudentsWorking Adults
C11
181 משפטים
The Limit (do not use L'Hospital rule)
Daily ConversationUniversity Students
C150 משפטים
GCSE Physics - Energy Stores, Transferring Energy & Work Done
Daily ConversationUniversity Students
C16
108 משפטים
Homeostasis - How Your Body Keeps its Balance - Physiology Series
Daily ConversationUniversity Students
C1552 משפטים
The Professor Who Taught People How To Think (1962)
Daily ConversationUniversity StudentsWorking Adults
Understanding Physics and Language: A Unique Learning Context
The video explores how physics uses mathematics as its language, focusing on derivatives to describe change. This context—blending science and real-world scenarios like speeding tickets—creates engaging dialogue that’s perfect for English speaking practice. The mix of technical terms (e.g., "derivatives," "limits") and casual language ("OH NO!") makes it ideal for building both academic and conversational skills, useful for tests like IELTS speaking practice.
Top 5 Phrases for Daily Communication
- "closely connected" – Useful for explaining relationships (e.g., "Work and rest are closely connected").
- "get back on the road" – A common phrase for resuming activities (e.g., "After the break, let's get back on the road").
- "foot still on the gas" – Figuratively means continuing effort (e.g., "She kept her foot on the gas to finish the project").
- "get closer to the right number" – Helps discuss progress (e.g., "With practice, you'll get closer to the right answer").
- "slow way down" – A casual way to advise caution (e.g., "Slow way down—there's a stop sign ahead").
Step-by-Step Shadowing Guide for This Video
Shadowing (repeating speech in real time) improves fluency and pronunciation. Here’s how to tackle this video:
- Listen first, then mimic: Watch the video once to grasp the story. Pause after short segments (e.g., "Velocity is a measure...") and repeat, focusing on intonation (e.g., the urgency in "OH NO!"). This builds natural rhythm, key for shadow speech.
- Break down technical terms: Words like "derivatives" or "integrals" can be tricky. Say them slowly, emphasizing syllables ("de-riv-a-tives"), then blend them into sentences. This helps with clarity in academic contexts.
- Focus on casual phrases: The dialogue includes conversational bits ("you know, just in case"). Repeat these to sound more natural—critical for IELTS speaking practice.
- Use pauses strategically: The speaker pauses before explaining key ideas (e.g., "But let's start with derivatives"). Mimic these pauses to improve pacing, making your speech easier to follow.
- Practice daily with short clips: A 5-minute segment daily is more effective than long sessions. Use this video as a shadowing site to build consistency, and track progress by comparing your repeats to the original.
By combining science content with targeted shadowing, you’ll boost both English skills and physics knowledge—proving learning can be both practical and fun.
דקדוק בסרטון הזה
המבנים שהדובר משתמש בהם הכי הרבה, עם המילים המדויקות מהסרטון:
| מבנה | בסרטון |
|---|---|
| הווה מושלם ממושך (Present perfect continuous) have/has been + -ing — פעולה שהתחילה בעבר ועדיין נמשכת עכשיו | we've been talking · have been using · you've been driving |
| סביל (Passive voice) be + past participle — הדגש הוא על מה שקורה, לא על מי שעושה את הפעולה | was broken · are based · is raised |
| משפטי זיקה (Relative clauses) who / which + clause — מידע נוסף על אדם או דבר | velocity, which is · second, which is · Integrals, which will |
| הווה מושלם (Present perfect) have/has + past participle — פעולה שקרתה בעבר ועדיין יש לה חשיבות או השפעה עכשיו | have come · haven't even talked |
מהי טכניקת השאדואינג?
שאדואינג היא טכניקת למידת שפה מבוססת מדע שפותחה במקור להכשרת מתורגמנים מקצועיים ופופולרית על ידי הפוליגלוט ד"ר אלכסנדר ארגואלס. השיטה פשוטה אך עוצמתית: אתה מקשיב לאודיו באנגלית ילידית וחוזר עליו בקול רם מיד — כמו צל העוקב אחרי הדובר עם עיכוב של 1–2 שניות בלבד. בניגוד להאזנה פסיבית או תרגילי דקדוק, שאדואינג מכריח את המוח והשרירים בפה לעבד ולשחזר דפוסי דיבור אמיתיים בו זמנית. מחקרים מראים שזה משפר משמעותית את דיוק ההגייה, האינטונציה, הקצב, הדיבור המחובר, הבנת השמיעה ושטף הדיבור — מה שהופך אותו לאחת השיטות היעילות ביותר להכנה לIELTS Speaking ולתקשורת באנגלית בעולם האמיתי.