Introduction to Acceleration with Prius Brake Slamming Example Problem
Summary
TLDRIn this educational video, Mr. P teaches the concept of acceleration using the Flipping Physics format. The class begins with the definition of acceleration as the change in velocity over time, represented by 'a'. The students, Billy and Bobby, engage in a discussion to understand the concept of 'delta', which signifies the difference between final and initial values. They explore the dimensions of acceleration in SI units, leading to the conclusion that acceleration is measured in meters per second squared (m/sec^2). The lesson continues with an example problem involving a car stopping due to an obstacle, emphasizing the importance of considering both magnitude and direction in acceleration. The students learn to convert units and apply the formula for acceleration to solve the problem, highlighting the need for careful unit conversion and attention to detail.
Takeaways
- 📚 The symbol for acceleration is 'a', and it's calculated as the change in velocity (delta v) over the change in time (delta t).
- 🔍 'Delta' represents the difference between final and initial values, a concept that applies to various physics calculations.
- 🧮 Acceleration is expressed in meters per second squared (m/sec^2), which is derived from the units of velocity change over time change.
- 🌟 The script humorously mentions alternative units for acceleration like km/hr^2 or furlongs/fortnight^2, emphasizing the standard use of m/sec^2.
- 🚗 An example problem involves calculating the acceleration of a car that stops from 36 km/hr in 1.75 seconds, highlighting the application of the concept.
- 🔄 The importance of converting units is stressed when calculating acceleration, ensuring that velocity is in meters per second (m/sec).
- 🤓 The script corrects a mistake in the example problem, emphasizing the need to use the change in velocity (final minus initial) in calculations.
- 📉 The final velocity in the example is zero because the car stops, which is a critical piece of information for calculating acceleration.
- ⚖️ The correct calculation of acceleration in the example results in -5.7 m/sec^2 East, indicating a decrease in velocity and the direction of the acceleration.
- 📝 The script concludes with advice to be careful and methodical in physics problem-solving, underlining the importance of attention to detail.
Q & A
What is the formula for acceleration as described by Mr. P.?
-The formula for acceleration is a = delta v / delta t, where delta v represents the change in velocity and delta t represents the change in time.
How do you calculate the change in velocity?
-The change in velocity (delta v) is calculated as the final velocity minus the initial velocity. In this case, delta v = velocity final - velocity initial.
What are the SI units for acceleration?
-The SI units for acceleration are meters per second squared (m/sec^2), which can also be written as m/sec/sec.
Why does Mr. P. emphasize the need for both magnitude and direction in acceleration?
-Acceleration, like velocity and displacement, is a vector quantity, meaning it has both magnitude (the value) and direction. It’s important to include both when solving physics problems to provide a complete answer.
How does Billy simplify the dimensions for acceleration?
-Billy explains that since acceleration is velocity (m/sec) over time (sec), the result is m/sec^2 after simplifying by multiplying m/sec by 1/sec.
Why did Bo initially get the wrong answer when calculating acceleration?
-Bo initially got the wrong answer because he used the initial velocity of 36 km/hr directly without converting it to the correct SI units (m/sec). This caused a dimensional mismatch in the calculation.
How was the velocity converted from km/hr to m/sec?
-The velocity was converted by multiplying 36 km/hr by 1000 m/km and dividing by 3600 sec/hr, resulting in 10 m/sec.
What mistake did Bo make regarding the change in velocity?
-Bo mistakenly used 36 km/hr as the change in velocity instead of recognizing that it was the initial velocity. The final velocity was actually 0 since the car came to a stop, so the correct change in velocity was 0 - 10 m/sec.
What was the final correct acceleration value after all corrections?
-The final correct acceleration value was -5.7 m/sec^2, with the negative sign indicating deceleration, and the direction being East.
Why does Mr. P. stress slowing down and writing everything down during problem-solving?
-Mr. P. emphasizes taking time and writing everything down because many students rush through problems and make mistakes. Being careful ensures that important steps, such as unit conversions and correctly identifying variables, are not missed.
Outlines
📚 Introduction to Acceleration
The script opens with a classroom setting where Mr. P introduces the concept of acceleration to his students. The symbol for acceleration is 'a', and it's defined as the change in velocity (delta v) over the change in time (delta t). Bo explains that delta represents the difference between final and initial values. Mr. P emphasizes the importance of understanding the concept of 'delta' as it frequently appears in physics. The class then explores the dimensions of acceleration, which are derived to be meters per second squared (m/sec^2). The conversation also touches on the idea that acceleration, like velocity and displacement, has both magnitude and direction. An example problem is introduced where Mr. P's car decelerates to a stop, and the students are tasked with calculating the acceleration.
🚗 Calculating Acceleration with Correct Units
In this segment, the students attempt to calculate the acceleration of Mr. P's car as it stops due to an unexpected basketball in the road. Initially, Bo makes a mistake by not considering the change in velocity but rather using the initial velocity directly. Mr. P corrects this by emphasizing that the change in velocity (final velocity minus initial velocity) should be used. The class then realizes that the initial velocity must be converted from km/hr to m/sec to match the units of the change in time (seconds). After the conversion, the correct calculation is made, and the acceleration is found to be -5.7 m/sec^2 East, indicating the magnitude and direction of the car's deceleration. The lesson concludes with a reminder to be careful with unit conversions and to include both magnitude and direction in the final answer.
🎥 Behind-the-Scenes with Flipping Physics
The final paragraph provides a behind-the-scenes look at the production of the Flipping Physics video. It includes outtakes and additional footage of the actors, showcasing the more casual and humorous side of the educational content creation process. The students and Mr. P engage in light-hearted banter, and there's a focus on the filming process with multiple cameras running. The paragraph ends with a voiceover comment about the importance of emotion in the videos, highlighting the human element of educational content.
Mindmap
Keywords
💡Acceleration
💡Velocity
💡Delta (Δ)
💡Displacement
💡Base SI Dimensions
💡Magnitude
💡Direction
💡Initial and Final
💡Units Conversion
💡Significant Figures
Highlights
Mr. P begins the class by explaining that acceleration is the change in velocity over time, symbolized as 'a'.
Bo defines delta as 'final minus initial,' noting its relevance to velocity and time changes.
Billy works through the dimensions of acceleration, concluding it as m/sec^2 by multiplying and flipping the time units.
Mr. P emphasizes that acceleration, like velocity and displacement, has both magnitude and direction.
The class works on an example where Mr. P brakes his car to avoid a basketball, calculating the acceleration using the formula a = delta v/delta t.
A mistake in the initial calculation occurs when Bo incorrectly uses the initial velocity as the change in velocity.
Billy identifies the final velocity of the car as zero because it comes to a complete stop.
Mr. P corrects the students by noting that the change in velocity must be calculated as the difference between final and initial velocities.
Bo sighs in frustration as Bobby converts the initial velocity of 36 km/hr to 10 m/sec for the proper calculation.
Billy performs the final calculation, yielding -5.7 m/sec^2 East for the car’s acceleration after applying the correct values.
Mr. P highlights the importance of adding direction when reporting acceleration values.
Mr. P cautions students against rushing through physics problems, advising them to slow down and write everything down carefully.
The problem-solving process emphasizes the conversion of units to ensure that dimensions align properly.
Mr. P concludes the lesson with a reminder that acceleration, like displacement and velocity, requires both magnitude and direction for completeness.
As a lighthearted end, the class enjoys playful banter, and Mr. P acknowledges the use of three video cameras for the session.
Transcripts
Bo: Hi, guys. Billy: Hey, Bo. Bobby: Hi, Bo.
♫ (lyrics) Flipping Physics ♫
Mr. P.: Ladies and gentlepeople, the bell has rung, therefore
the class has begun and, therefore, you should be
seated in your seat and ready and
excited to learn about acceleration.
Billy: Yeah. Bobby: Yeah. Bo: (sigh) Let's do it.
Mr. P.: The symbol for acceleration is a lowercase "a",
and the a=delta v/delta t, or the change
in velocity over change in time.
Remind me, Bo, what does delta v
or the change in velocity mean?
Bo: Delta means final minus initial,
that's what it always means. We saw that with
the change in position and with change in time.
Mr. P.: Yes, that's true, and delta
will continue to come up quite often.
Bo: So, delta v means the change in velocity
or the final velocity minus the initial velocity.
Mr. P.: Yes, the change in velocity is equal to
velocity final minus velocity initial,
and also the change in time then
is going to be time final minus time initial.
Let's now work out the dimensions
for acceleration in base SI dimensions.
Billy, can you work on that, please?
Billy: Well, acceleration equals
change in velocity over change in time,
so in the numerator we should have m/sec,
and in the denominator, we should just have seconds.
Oh, we get to flip the guy and multiply.
Mr. P.: By whom do we need to flip and multiply?
Billy: The guy is second...no, oh wait, wait, no
sec/1, so we get m/sec multiplied by 1/sec,
and that works out to be m/sec^2.
Mr. P.: Exactly right.
Acceleration works out to be in m/sec^2.
Some people like to call it m/sec/sec,
I myself prefer m/sec^2.
Both are correct, and they're the same thing,
m/sec^2 and m/sec/sec, but again, I prefer m/sec^2.
Also, we could have km/hr^2, or furlongs/fortnight^2,
but usually we see it in base SI dimensions,
which works out to be m/sec^2.
Next, please remember that acceleration
is in terms of velocity, and velocity
is in terms of displacement and,
therefore, just like displacement and velocity,
acceleration has both...?
Bobby: Magnitude and direction. Billy: Oh, yeah. Magnitude and direction.
Mr. P.: Yes, please remember that acceleration,
just like velocity and displacement,
has magnitude and direction.
Again, acceleration has both magnitude and direction,
magnitude being the amount or the value of,
and direction being, well, the direction.
Bo, let's work on an example problem.
Could you please read it?
Bo: Mr. P is driving his Prius at 36 km/hr East
when a basketball appears bouncing
across the street in front of him.
His gut reaction is to slam on the brakes.
This brings the vehicle to a stop in 1.75 seconds.
What was the acceleration of the vehicle?
(car engine) (basketball dribbling)
(brakes screeching to a halt, child crying)
Geneve: I lost the ball again.
Bo: I like that. Bobby: Yeah.
Mr. P.: Thanks. Just so you know, this 36 km/hr,
some of you might not be familiar with how fast that is,
so let's convert to m/hr, and there are
1609 meters in one mile, therefore...
therefore, we can take our 36 km/hr,
multiply it by 1000 m over 1 km, the km cancel out,
we can then multiply it by 1 mile/1609 m,
the meters then cancel out, and we're left with miles/hr,
and that works out to be 22.3741 or approximately 22 miles/hr,
just to give you an idea of how fast
we're moving at the beginning here.
Bobby, if you could please translate...and Bo,
could you please read again.
Bo: Mr. P. is driving his Prius at 36 km/hr East
when a basketball appears bouncing
across the street in front of him. Bobby: Please stop.
Change in velocity equals 36 km/hr East.
Mr. P.: Bo, please continue.
Bo: His gut reaction is to slam on the brakes.
This brings the vehicle to a stop in 1.75 seconds.
What was the acceleration of the vehicle?
Bobby: Change in time equals 1.75 seconds,
and acceleration, or little "a", is equal to ?.
Mr. P: Ok, Bo, how do you want to solve the problem?
Bo: Again, we start with the equation a = delta v/delta t.
Bobby: Remember words, not letters.
Bo: Yeah, sorry. Acceleration equals
the change in velocity over the change in time,
and we know both of those numbers,
so we just plug in the numbers, 36/1.75,
and that gives us 20.5714 or with 2 sig figs, 21 m/sec^2.
Mr. P.: (sigh) I'm sorry, there are
so many things wrong with this,
I don't even know where to start.
I guess actually let's start by going back
to the givens, where we started here.
Who can tell me something that's
wrong with one of our givens?
Bo: 36 km/hr. That's not the change in velocity,
that's actually the velocity at the beginning,
the initial velocity.
Billy: We also know the final velocity of the car,
because the car stops, then the final velocity is zero.
Mr. P.: Correct. This 36 km/hr East wasn't
the change in velocity, that was velocity
at a specific time, the velocity at
the very beginning, or the velocity initial.
We also know that the velocity final is equal to 0,
because this car comes to a stop.
Therefore, this is not correct.
We need to plug in the change in velocity
or velocity final minus velocity initial.
We can leave the change in time at the bottom,
because we do know that the time duration is 1.75 sec,
that's not the time initial or time final,
that's the time duration.
Therefore, we need to go back to here,
erase this, and substitute in
velocity final minus velocity initial.
Now, if you look at this equation, we know
the velocity initial, we know the velocity final,
and we know the change in time.
We can just plug in the numbers.
So, we can just plug in our numbers at this point
and we get zero minus 36, divided by 1.75.
Unfortunately, when we do that, we just get
the negative of the number we got before, -21,
but unfortunately we're going to
have an issue with our dimensions.
We have 36 km/hr as our velocity initial,
and our change in time is 1.75 sec.
So, we get km/hr divided by seconds.
The dimensions there are going to work out to be km/hr sec,
and that doesn't make any sense.
Bobby: We need to convert the 36 km/hr
in m/sec before we use it in the equation.
Bo: (exasperated sigh)
Bobby: (laughs) And so, 36 km/hr...we need to multiply it
by 1 hr/3600 sec to cancel out the hours,
and multiply it by 1000 m over 1 km to cancel out the km.
Give me a second.
That actually worked out to exactly 10 m/sec.
Mr. P.: Great! Now we can go back to our equation
and rather than using initial velocity of 36 km/hr East,
we're going to use our initial velocity of 10 m/sec
and the dimensions will work out fine now.
So, we end up with our velocity final zero,
minus our velocity initial of 10 m/sec,
divided by our change in time 1.75 sec.
And what do we get now for an answer?
Billy: We get -5.7143, which rounds to,
with two significant digits, -5.7 m/sec^2.
Mr. P.: (sigh)
Billy: Oh, -5.7 m/sec^2 East.
You need to add East, the direction.
Mr. P.: Yes, please include the direction for acceleration.
Remember, acceleration, just like displacement of velocity,
has both magnitude and direction.
Therefore, for an answer you need to give acceleration
with the direction, -5.7 m/sec^2 East.
-5.7 m/sec^2 is the magnitude, East is the direction.
Now, I know this problem was relatively simple.
However, a lot of students still make mistakes with it
because they just want to rush through the problem.
Don't. Slow down, write everything down.
Be careful...please.
Ladies and gentlepeople, I hope
you enjoyed learning with me today.
I enjoyed learning with you.
Voiceover: Lecture notes are available
at flippingphysics.com.
Please enjoy lecture notes responsibly.
(basketball dribbling)
Voiceover: I like the emotion, the emotion is good.
The, (without emotion) "Oh, I lost the ball."
Geneve: Oh, dang, I lost the ball. Voiceover: A little bit better (laughter).
Mr. P.: We have three video cameras running at the moment.
Geneve: Buggy, wuggy, wuggy. Geneve: Did they video tape that? Mr. P.: Yep.
(brakes)
Mr. P.: (laughter) Ryan: Yahoo! Mr. P.: How did that go?
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