Suppose you have a car,
its a thousand kilograms and you're driving at 50 kilometers per hour.
The question is, how much kinetic energy does that car have?
And then if you double the speed, how much kinetic energy,
how much would the kinetic energy change?
So first, just try this yourself and see if you can figure out
what the kinetic energy is of a vehicle with this mass and this velocity
using the equation that we just introduced.
Hopefully when you did that, you came up with something like this.
We have an object which is 1000 kilograms in mass.
And then we also give this object a velocity
which we said was 50 kilometers per hour.
What we would do to find the kinetic energy,
let's say this is 1/2 the mass times the velocity of our object squared.
And you might be tempted to just write 1/2 times 1000,
times the velocity which is 50 squared.
This a very common pitfall,
so I wanted point it out and write it exactly as I have,
and this would be incorrect if you did it exactly like this.
And the reason is we have to be careful about our units.
We have units here of a velocity, v, kilometers per hour,
which is not going to be on our standard units of meters,
and seconds and kilograms.
And so, these units, the units of this quantity will not come out to be joules
if we just put together the kilograms with kilometers and hours.
So the first thing we have to do,
we want to get units of joules for our kinetic energy,
is to first convert the units of our velocity
into standard units of meters per second.
So let's do that very quickly.
If the velocity is 50 kilometers per hour,
we're gonna do a quick unit analysis here.
And say that this is equal to, the first thing we need to do is,
let's try to convert these kilometers.
So we'll say that there are thousand meters in a kilometer.
And we know to put the kilometers on the bottom
so that we can cancel our units of kilometers.
And then we need the number of seconds in an hour.
So let's say this one hour with 3600 seconds in an hour.
So this will cancel our units of hours and nicely leave us
with units of meters per second.
And so this is how our unit analysis would work.
So let's start cancelling some zero's here.
So we have two zero's from the 1000, two zero's from the 36.
And if you actually do this out
and calculate this you'll get a number that is something like close to 14.
A little bit less than 14 if you did this yourself.
So now, we're just gonna take this number 14,
which has our correct units of meters per second
and put this quantity into our kinetic energy expression.
So let's do that, we have kinetic energy is equal to 1/2,
1000 times 14 squared.
14 squared is 196, so we simply have 1/2 times 1000 times 196.
If you write all this out, you should get something like 98.000 joules.
And you notice this is quite a big number,
and often when we're talking about energy,
we'll be dealing with big numbers and energy,
thousands of joules or even millions of joules.
And so we we'll often write instead
because we're dealing with such big numbers, kilojoules for example.
So we could write this instead as 98 kilojoules.
So either one of these answers would be correct,
but be careful especially in an exam setting.
If you're trying to answer and they ask you whether it's 98.000 or 98.
Then you will look at the units they gave you,
because the very common thing might be for them to say,
is it 98.000 kilojoules.
If you don't notice the KJ there, you might get the answer wrong
if you're not careful about which units are being given.
So either one of these would suffice but again keep J for joules
and KJ for kilojoules separate.