When you mow the lawns, you do work

The longer the grass is the more work you have to do

The muddier the ground, the more force you have to push with to move the lawnmower, and the more work you do

The bigger the lawn, the more work you do

These are the two big things with work. How much force you have to apply, and how far you have to go

So work is Force applied across a distance

Work = Force times Distance

Work is measured in Joules

Force in Newtons

Distance in Meters

W = F d

Another way of looking at this is as energy

Work = Total Energy

So the bigger the lawns you have to mow, the more energy you will use

The more energy you will transform

The more energy you will 'burn' 

The more food you will want to eat afterwards

More work = more energy

Less work = less energy

Power is how quickly you can do work

The more powerful you are, the faster you can do the work

How long would it take to mow your lawn with one of the lawnmowers in the clip to the right?

To be powerful, you have to be able to do the work faster. If the Rock, Dwaine Johnson and I were to lift 4 20kg weight plates across the room, I would carry each individually, and he would carry them all at once. So it would take me four times longer. So, the Rock is at least 4 times more powerful than I am

In the 'Hammock Run" clip,  I am doing the same as I was in the "Hammock Walk" clip, the same amount of work, but in far shorter time. So I am more powerful in the Hammock Run than I was in the Walk

So, Work and Time are the important factors when it comes to the Power

You are more Powerful if you can do the Work in less time

Power is thus Work divided by time

Power = Work / Time

P = W/t

Power is measured in what? Watts

Work is measured in Joules 

Time is in seconds (as it always is in Science, Science Seconds)

So

Watts = Joules / second

Watts = Joules per second

So your 1000Watt Gaming PC will use up to 1000 Joules per second when it is pushing it

Your 20Watt light bulb will only transform 20 joules of electrical energy into heat and light energy per second.

In the bench press example, Eddie Hall will transform 935 Joules of his chemical potential energy into Kinetic Energy per second of bench press.

My Holden Commodore 2017 SV6 II car is rated at 280HP or 210kW. At its maximum push, it will transform 210,000 Joules of petrol's chemical potential energy into kinetic energy per second.

As explained above, because Work(J) and Change in Energy (J) are the same thing, we can also apply this to the power calculations

Power = Work / Time

P = W/t

P =  ΔE / t

Thus we can rearrange Power to calculate Total Energy

    ΔE = P x t

Lets take a 700Watt toaster.  P = IV 

Every second it will transform 700 Joules of electrical energy into heat and light energy. 

But it won't toast your bread in one second. So it needs to run for several seconds

Lets take a cyclist. 

He can transform 700 Joules of chemical potential energy at his maximum push into Kinetic energy.  P = W/t 

Notice we have two formulas for power

Electrical power: P = IV 

Mechanical Power:     P = W/t

This is because they are just how much energy is transformed per second. 1 watt is the energy required to move 6 quintillion electrons with 1 Volt. 1watt is also the amount of energy required to move 100 grams by 1 meter.

Energy is interchangeable.  So you can use electrical power to get mechanical power, like spinning the fan in your PC. Or to drive an electric car. Likewise, you can use mechanical power to get electrical power. Like this spinning of wind turbines to generate electricity, or the spinning of turbines in a hydroelectric dam

So 

Electrical power = Mechanical Power

But not exactly, due to some energy lost as thermal energy