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?