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### Course: MCAT > Unit 9

Lesson 2: Translational motion and calculations- Speed and velocity questions
- Acceleration questions
- Calculating average speed and velocity edited
- Solving for time
- Displacement from time and velocity example
- Instantaneous speed and velocity
- Acceleration: At a glance
- Acceleration
- Airbus A380 take-off time
- Airbus A380 take-off distance
- Why distance is area under velocity-time line
- Average velocity for constant acceleration

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# Acceleration

Acceleration (a) is the change in velocity (Δv) over the change in time (Δt), represented by the equation a = Δv/Δt. This allows you to measure how fast velocity changes in meters per second squared (m/s^2). Acceleration is also a vector quantity, so it includes both magnitude and direction. Created by Sal Khan.

## Want to join the conversation?

- how do u find momentum(16 votes)
- Momentum is found by multiplying the mass which is moving by its velocity. Momentum is typically represented by the variable "p", so the equation for finding momentum would be "p=mv".(46 votes)

- Ok so I just wanna make sure I understand this correctly: So the reason seconds is squared is because it is seconds PER second, right?(15 votes)
- I think you get the point, but it may be easy to be misinterpret. If I were to try to figure out the number of units of time per another unit of time. It might be difficult to get from how it is said, exactly, but it's because you are taking velocity (which is already in meters per second) and dividing it further by another unit of seconds, meaning you effectively have
`((m/s)/s)`

.(6 votes)

- so speed without direction is a scalar quality and velocity is speed with direction making it a vector quality, right?(13 votes)
- yes as long as a number assosiated with how fast an object is moveing has a dirction it is a vector quality otherwise its a scaler quality(5 votes)

- As I know lots about cars, I know that accelerating in the beginning is easier than when you go higher because engine needs to maintain the old speed + add new speed (accelerate)......I am assuming the 20mph/second^2 to be the
**average**of the three seconds of acceleration. For example, say that the car accelerated up to 23mph in the first second, 21 mph in the 2nd second, and 19mph in the 3rd second. It wouldn't have been exactly 20, 20, 20......So my question is, is there any way we can find the three possible**exact**values of each second of acceleration according to the info I have just given using physics?(12 votes)- You're technically referring to average values for each second as well. From the initial set of information described, it is not possible to get back to more detailed information about each second or the more desirable instantaneous acceleration (the slope of the velocity graph at a particular point) from which it's possible to get any other information about the average acceleration overall or over any sub-period within said range (see integral calculus for details on how).

Short of it, no. Averaging a set of data hides completely the details interior to it so you can't reverse it.(6 votes)

- At6:08, how did he cancel out the hour from the denominator ?(3 votes)
- To be honest, I find this explanation is confusing since it mixes incomplete explanations about acceleration and unit conversion.

Your question is related to the second topic (unit conversion) and is not explained sufficiently here, I think. For some reason the lecturer is trying to put the final result in miles/second/second. Do not ask me why exactly, I would stick with miles/hour/second which are valid units, or go to meter/second/second (International units).

Anyway, you have miles/hour/second and you want to change then hours to seconds.

The way to do this is: You can always multiply by a fraction equal to 1 (which would change nothing). So your trivial multiplying factor would be 1 hour / 1 hour but since 3600 seconds equals to 1 hour, this can be written as well as 1 hour / 3600 which is a convenient conversion factor from hours to seconds. Then hour units cancel out when multiplying and you got your result in seconds.

You may consider instead the reverse fraction: 3600 seconds / 1 hour, but you can discard this since it would not cancel out.

This is general procedure for any units conversion and can be applied multiple times until converting to convenient units.(7 votes)

- What about deceleration? what's the definition and how do you calculate it? is it any different from calculating acceleration? except for maybe some negative values?(4 votes)
- Deceleration is just acceleration, where the acceleration vector is pointing in the opposite direction in respect to the velocity vector. Usually in physics we only say acceleration but give a direction (because it is a vector).

For example: if you are moving at 3m/s to the right and accelerating at -1m/s/s, then you are "decelerating" by 1 m/s every second. After 3 seconds you will have decelerated to 0 m/s.

Do you understand? If not commment and we can continue the conversation.(10 votes)

- I watched all the videos in this chapter but couldn’t find about the formula xf=xi+vit+1/2at^2 which was appeared at the position acceleration and velocity questions. Can I ask the explanation of that formula?(8 votes)
- If acceleration
**a**is constant, it means that the velocity**v**is increasing linearly with respect to time (**a**= (**vf**-**vi**)/**t**or**vf**=**vi**+**a**.**t**), where**vi**is the initial velocity at time 0 and**vf**is the final velocity at time**t**. If velocity was fixed, then distance**x**will change linearly. But in this case velocity is changing linearly with time**t**, so the distance is changing quadratically (power of 2) with respect to time, then distance**x**=**xi**+ b.**t**+ c.**t**^2, where**xi**is initial distance at time = 0, b and c are constants. We need to solve and find b and c which are related to**vf**,**vi**and**a**.

One way is to use differentiation. If we differentiate**x**with respect to**t**, we get velocity**v**= (change in**x**)/ (change in**t**).**x**=**xi**+ b.**t**+ c.**t**^2, after differentiation we get**v**= b + 2.c.**t**. comparing with the**vf**=**vi**+**a**.**t**, final velocity or velocity at time**t**is**vf**, b=**vi**,**a**= 2.c and c =**a**/2.

Replace b and c in the equation, and distance**x**at time**t**is**xt**, we get**xt**=**xi**+**vi**.**t**+ (**a**/2).**t**^2

This equation is for the distance**x**at time**t**, when initial distance is**xi**, initial velocity is**vi**, and acceleration is**a**.(1 vote)

- what is a porsche?(0 votes)
- A Porsche is a make of German sports car.(16 votes)

- is acceleration always constant(3 votes)
- No, if the force is not constant then the acceleration is not constant. Both gravity and EM forces vary with position.(7 votes)

- I'm trying to understand what all of these kinematic formulas mean. So playing around with some graphs, I came up with a question. I am sure the answer is simple, but I don't yet know it.

Imagine that I start with a velocity of 0 and accelerate for four seconds (constant), and have a final velocity of 3 m/s.

Therefore, constant acceleration would = 3/4 m/s². The magnitude of the graph over this time period would = √3²+4².

What does this magnitude represent, and how would it be used?(4 votes)- What do you mean by the "magnitude of the graph"? You are doing (vf^2 + t^2)^(1/2)? Why would you want to do that?(5 votes)

## Video transcript

In this video, I want to talk a
little bit about acceleration. And this is probably
an idea that you're somewhat familiar
with, or at least you've heard the term
used here or there. Acceleration is just the
change in velocity over time. Probably one of the most typical
examples of acceleration, if you're at all
interested in cars, is that many times
they will give you acceleration numbers, especially
for sport cars, actually all cars if you look
up in Consumer Reports, or wherever they give the
stats on different cars. They'll tell you something like,
I don't know, like a Porsche-- and I'm going to make up
these numbers right over here. So let's say that we
have a Porsche 911. They'll say that a Porsche 911,
they'll literally measure it with a stopwatch, can go
0 to 60 miles per hour. And these aren't
the exact numbers, although I think it's
probably pretty close. 0 to 60 miles per hour
in, let's say, 3 seconds. So, although officially what
they're giving you right here are speeds, because
they're only giving you magnitude and no
direction, you can assume that it's in
the same direction. I mean, We could
say, 0 miles per hour to the east to 60 miles per
hour to the east in 3 seconds. So what was the
acceleration here? So I just told you the
definition of acceleration. It's change in
velocity over time. So the acceleration-- and
once again acceleration is a vector quantity. You want to know not only
how much is velocity changing over time, you also care
about the direction. It also makes sense
because velocity itself is a vector quantity. It needs magnitude
and direction. So the acceleration
here-- and we're just going to assume
that we're going to the right, 0 miles per
hour and 60 miles per hour to the right-- so it's going
to be change in velocity. So let me just write it
down with different notation just so you could
familiarize yourself if you see it in the
textbook this way. So change in velocity. This delta symbol right
here just means "change in." Change in velocity over time. It's really, as I've
mentioned in previous videos, it's really time is
really a change in time. But we could just
write time here. This 3 seconds is
really change in time. It might have been, if you
looked at your second hand, it might have been 5 seconds
when it started, and then my 8 seconds when it stopped, so
it took a total of 3 seconds. So time is really a
change in seconds. But we'll just go with time
right here, or just with a t. So what's our
change in velocity? So our final velocity
is 60 miles per hour. And our original velocity
was 0 miles per hour. So it's 60 minus
0 miles per hour. And then, what is our time? What is our time over here? Well, our time is, or we could
even say our change in time, our change in time is 3 seconds. So this gives us 20 miles
per hour, per second. Let me write this down. So this becomes,
this top part is 60. 60 divided by 3 is 20. So we get 20. But then the units are
little bit strange. We have miles. Instead of writing MPH, I'm
going to write miles per hour. That's the same thing as MPH. And then we also, in the
denominator, right over here, have seconds. Which is a little bit strange. And as you'll see, the
units for acceleration do seem a little bit strange. But if we think it
through, it actually might make a little
bit of sense. So miles per hour. And then we could either
put seconds like this, or we could write per second. And let's just think
about what this is saying, and then we could get
it all into seconds, or we could all get into
hours, whatever we like. This is saying that every
second, this Porsche 911 can increase its velocity
by 20 miles per hour. So its acceleration is 20
miles per hour, per second. And actually, we should
include the direction, because we're talking
about vector quantities. So this is to the east. So this is east, and then
this is east right over here-- just so we make sure that
we're dealing with vectors. You're giving it a
direction, due east. So every second it can
increase in velocity by 20 miles per hour. So hopefully, with
the way I'm saying it, it makes a little bit of sense. 20 miles per hour, per second. That's exactly what
this is talking about. Now we could also
write it like this. This is the same thing
as 20 miles per hour, because if you take
something and you divide by seconds, that's the
same thing as multiplying it by 1 over seconds. So that's miles
per hour-seconds. And although this
is correct, to me this makes a little
less intuitive sense. This one literally says it. Every second, it's increasing in
velocity by 20 miles per hour. 20 miles per hour increase
in velocity per second. So that kind of
makes sense to me. Here it's saying 20
miles per hour-seconds. So once again, it's
not as intuitive. But we can make this so it's
all in one unit of time, although you don't
really have to. You can change this
so that you get rid of maybe the hours
in the denominator. And the best way to get rid
of an hour in the denominator, is by multiplying
it by something that has hours in the numerator. So hour and seconds. And here, the smaller
unit is the seconds. So it's 3,600 seconds
for every 1 hour. Or 1 hour is equal
to 3,600 seconds. Or 1/3600 of an hour per second. All of those are legitimate
ways to interpret this thing in magenta
right over here. And then you multiply, do a
little dimensional analysis. Hour cancels with hour. And then will be
equal to 20/3600. 20/3600 miles per
seconds times seconds. Or we could say,
miles-- let me write it this way-- miles per
seconds times seconds. Or we could say,
miles per second-- I want to do that in
another color-- miles per second squared. And we can simplify
this a little bit. Divide the numerator
and denominator by 10. You get 2/360. Or you could get,
this is the same thing as, 1/180 miles
per second squared. And I'll just
abbreviate it like that. And once again, this 1/180
of a mile, how much is that? You might want to
convert to feet. But the whole point
in here is, I just wanted to show you
that, well, one, how do you calculate acceleration? And give you a little bit
of a sense of what it means. And once again, this
right here, when you have seconds squared in
the bottom of your units, it doesn't make a ton of sense. But we can rewrite
it like this up here. This is 1/180 miles per second. And then we divide by
seconds again, per second. Or maybe I can write
like this, per second, where this whole thing
is the numerator. So this makes a
little bit more sense from an acceleration
point of view. 1/180 miles per
second, per second. Every second, this
Porsche 911 is going to go 1/180 of a
mile per second faster. And actually, it's
probably more intuitive to stick to the miles per
hour, because that's something that we have a little
bit more sense on. And another way to visualize it. If you were to be
driving that Porsche, and you were to look at the
speedometer for that Porsche, and if the acceleration
was constant-- it's actually not going to
be completely constant-- and if you look at
speedometer-- let me draw it. So this would be 10,
20, 30, 40, 50, 60. This is probably not what
the speedometer for a Porsche looks like. This is probably more analogous
to a small four cylinder car's speedometer. I suspect the Porsche's
speedometer goes much beyond 60 miles per hour. But what you would
see for something accelerating this fast is,
right when you're starting, the speedometer
would be right there. And that every second it would
be 20 miles per hour faster. So after a second
the speedometer would have moved this far. After another second
the speedometer would have moved this far. And then after another
second the speedometer would have moved that far. And the entire time
you would have kind of been pasted to the
back of your seat.