Question

Prove that one horse power is equal to 746watt

Answer 1

One pound is 4.44822 Newtons


so 550 foot pounds per seconds, converted to metric, is 550 x 0.3048 x 4.44822 Newton meters per second, which is 745.7 Newton meters per second, better known as Watts.


One foot is 0.3048 metres

1HP = 550 Foot Pound per second 
1 Pound = 4.44822 Newtons
1 Foot is 0.3048 Meters.
1 HP = 550 * 4.44822 * 0.3048 meters
1Hp = 745.69 Newton meter per second. 
A 1 hp motor cannot use less than 745.7 Watts so if it uses 1 kW it is about 75% efficient, which sounds about right for a motor of that size.