Acceleration
Acceleration Calculating the acceleration of a Porshe
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- In this video, I want to talk a little bit about acceleration.
- Acceleration.
- And this is probably an idea that you are somewhat familiar with
- or at least you've heard the term used here or there.
- Acceleration is just the change in velocity over time.
- Change in velocity over time.
- Probably one of the most typical examples of acceleration, if you are 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 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 we have a Porsche 911. 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, three seconds.
- In three seconds.
- So although officially what they are giving you right here are speeds
- cause they are only giving you magnitude and no direction,
- you can assume that it's in the same direction.
- And you can say 0 mph to the East to 60 mph to the East in 3 seconds,
- so what was the acceleration here?
- So I just told you the definition of acceleration -
- it's the 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 the velocity itself is a vector quantity.
- Needs magnitude AND direction.
- So the acceleration here,
- and we are just going to assume that we are going to the right,
- 0 mph and 60 mph to the right.
- So what is... It's going to be change in velocity - let me just write it down with different notation,
- just so you can familiarise yourself if you see it in a textbook this way.
- So change in velocity. This delta symbol right here just means 'change in'.
- Change in velocity over time. Over time.
- And it's really, as I've mentioned in previous videos,
- time, it's really change in time, but we can just write time here.
- This 3 seconds is really change in time.
- It might have been, you know, if you looked at your second hand,
- it might have been 5 seconds when it started and it might have been 8 seconds
- when it stopped, so it took a total of 3 seconds.
- So time - it's really a change in seconds. But we'll just go with time right here,
- Or we'll go with 't'.
- So what's our change in velocity?
- So our final velocity is 60 mph.
- Our final velocity is 60 mph.
- And our original velocity was 0 mph,
- so it's 60 minus 0 mph.
- 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.
- 3 seconds.
- So this gives us 20 mph 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 a 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,
- we also, right over here in the denominator
- have seconds.
- Which is a little bit strange.
- And, as you'll see, the units for acceleration do seem a little strange.
- But if we think it through, it actually might make a bit of sense.
- So miles per hour, and then we can either put seconds,
- like this, or we can write per second.
- And let's just think about what this is saying,
- and then we can get it all into seconds, or hours, whatever you like.
- This is saying that every second, this Porsche 911
- can increase its velocity by 20 mph.
- So its acceleration is 20 miles per hour per second.
- And actually we should include a direction, cause we're talking about vector quantities.
- So this is to the east.
- And 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 its velocity by 20 mph.
- So hopefully, the way I'm saying it makes a little bit of sense.
- 20 miles per hour per second.
- That's exactly what this is talking about.
- Now, we can also write it like this, this is the same thing
- as 20 miles per hour...
- Cause if you take something and divide it by second,
- that's the same thing as multiplying it by 1 over second.
- 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 that 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.
- Althought you don't really have to.
- You can change this so you can 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 units are seconds, so it's 3600 seconds for every 1 hour.
- Or, one hour is equal to 3600 seconds.
- Or, 1/3600 of an hour per second.
- All of those are legitime 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 you have...
- This will be equal to...
- This 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 you could say, miles per second...
- I want to do that in another colour.
- Miles per second squared.
- Miles per seconds... Miles per second squared.
- And we can simplify this a little bit.
- Divide the denominator and numerator by ten.
- You get 2 over 360.
- Or you could get.. This is the same thing as 1 over... 1 over 180.
- Miles per second squared. Per second squared.
- I'll just abbreviate like that.
- And once again, this doesn't make...
- 1 180th of a mile. How much is that?
- You might want to convert it to feet,
- but the whole point here is,
- I just wanted to show you that
- well, one, how do you calculate acceleration,
- and give you a little bit of sense what it means.
- And once again, what you have here,
- when you have seconds squared in the bottom of the units,
- it doesn't make a ton sense, but we could rewrite it like this up here.
- This is 180... or 1 / 180 miles per second...
- and then we divide by seconds again: per second.
- Or maybe I can write it 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.
- One over 180 miles 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,
- cause that's something that we have a little bit more sense on.
- And another way to visualize it.
- Another way to visualize it.
- If you were driving that Porsche, and
- you were looking at the speedometer of that Porsche,
- and if the acceleration was constant,
- it's actually not going to be completely constant,
- and if you looked at this 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 mph, but you would see, for something
- accelerating this fast, is right when you're starting,
- the speedometer would be right there.
- And then every second, it would be 20 mph 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.
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