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Velocity
Velocity
Mr Cowley Lecture 2: Velocity
Mr Cowley Lecture 2: Velocity
Above is a Short lecture about the Velocity of a person who has the munchies
Velocity = Distance / Time
Velocity = Distance / Time
The calculation for Speed and for Velocity is exactly the same
How fast are you going?
Well measure a distance
For instance Usain Bolt and James Corden are going to run 100 meters
So they run the same distance
The difference between them is how much time it takes them to run that distance
It takes Usain Bolt 11 seconds
It takes James Corden 15 seconds
So who was faster? - Usain Bolt
How fast was he? What was his Velocity?
They both ran 100 meters
Usain Bolt ran 100 meters in 11 seconds
James Corden ran 100 meters in 15 seconds
How many meters could they travel in each second? To do this we would take the distance they traveled and divide it by time. This would give the distance traveled (meters) in each unit of time (seconds)
Usain Bolt:
100 meters / 11 seconds = 9 meters per second
James Corden:
100 meters / 15 seconds = 6 meters per second
This shows that in each second, Usain Bolt covered more distance. So he was faster
The bigger the Velocity number the greater the distance covered per unit of time, so the faster they are going
If we look again at the maths, we see that we did:
meters / seconds = meters per second
This is the same on a Car's Speedometer:
kilometers / hour = kilometers per hour
What do these units represent?
distance / time = speed
Because speed and velocity are basically the same in most settings, we can say
distance / time = velocity
This is saying that velocity is distance divided by time
velocity = distance / time
We can also just use letters
v = d/t
So we can see that Velocity = distance / time
But what if we don't want to find velocity, rather we want to find distance or time?
For instance, I'm on the motorway at Pokeno and I want to head north to Whangarei. The Distance of road between the two points is 200km
I'm driving at 100km/h. Lets assume there is no traffic issues, no intersections etc so I can set the cruise control to 100km per hour
How much time will it take to travel the 200km?
Well, you would have worked that out in your head.
Traveling at 100kmph it would take 2 hours to travel 200km
What does that look like if you show your working?
I'd go:
200km / 100kmph = 2 hours
So what did I do? I went:
distance / velocity = time
What if I want to find distance?
Say my you borrow my car for 3 hours and drive the entire time. My car can tell me the average speed, it says that you drove it at 50km per h
So, how far did you travel?
Again, you kind of know how to calculate that without ever being told how to. You probably calculated it as 150km. But how did you do that? What was your working?
I'd go:
50kmph x 3 hours = 150km
So what did I do? I went:
velocity x time = distance
What we have done is called 'rearranging formula'
I personally think it is mostly intuitive, sometimes with hard questions, I'll insert simple maths first, like 6 = 3/2 and then rearrange that to find out how to rearrange the formula and then use the rearranged formula to work out the question.
You can also memorize triangles and use those to help with the rearranging. Below is the triangle. And to the side is a clip showing you how to do that. But I don't do it. :-)
Kinetic Energy
Kinetic Energy
Calculating Kinetic Energy
Calculating Kinetic Energy
This is a very good video - have a watch
Calculating Velocity from Kinetic Energy
Calculating Velocity from Kinetic Energy
You have to be able to calculate Velocity from a given Kinetic Energy and Mass Value
Gravitational Potential Energy
Gravitational Potential Energy
into Kinetic Energy
into Kinetic Energy
Excellence Level
When something falls, it speeds up
If a ball is at the top of a cliff and is then pushed off, at the top of the cliff it has maximum GPE, as it falls it gets closer to the ground, so it has less GPE, but it gets faster so it gets more EK. In the moment before it hits the ground it is at its maximum velocity, so almost all of the energy is converted into Ek and there is almost no GPE is left
Calculating Velocity when only given GPE information
Ep = m*g*h
Ek =½ *m* v2
Energy is Energy, so Ep is equal to Ek
Ep = Ek
This means that the energy that an object has before it falls from a height, will be the same as the amount of energy that object has when it hits the ground
m*g*h = ½ *m* v2
If we cancel 'm' as its on both side of the equation, then
g*h = ½ v2
Then we can rearrange to use Ep information to calculate the expected velocity if an object falls
2*g*h = v2
√(2*g*h) = v
This will give a theoretical velocity.
Thus, when given a height we can calculate the Velocity the object will be going when it gets to '0' height. This is summarized below in bold
Velocity when dropped from a given height:
√(2*g*h) = v
Or if we round g to 10 then 2x 10 is 20 so:
√(20*h) = v
The actual velocity will be less due to air resistance. Air resistance causes some of the energy to transform into heat energy
Rearranging Tool
Rearranging Tool
Can you show how to rearrange and isolate for Velocity?
What about Height or Gravity?
Converting GPE into Velocity
Converting GPE into Velocity
Ep = Ek + heat energy
Ep = Ek + heat energy
As stated in the Law of the Conservation of Energy, no energy is lost, only transformed.
Friction from atoms moving past each other will result in some Energy being transformed into Heat energy.
Have a play with the skateboarder, add 'bar graphs' and play with friction, see if this holds true
As you can see, with No friction, there is not Energy lost from the System as Thermal Energy - so the skateboard keeps going, forever.
Sometimes we try to minimize friction - streamline our cars, playing airhockey. Sometimes we try to maximize friction - super fat tires on cars, huge disc brakes.
All systems on earth will loose energy due to friction - air friction and contact friction.
Watch this video clip of a bowling ball and feathers being dropped with NO air frction
What do you think will happen when their is NO air?
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