Question

Would you be doing any more work by going up the stairs twice as fast?

Answer 1

No, because work done is equal to the product of force times distance. \[WD=F\times d\]In this case the work done is the energy expended to move your body mass against Earths gravitational field (which is providing the force on your body), up a certain distance. Therefore the work done will be equivalent to the change in gravitational potential energy or put simply \[WD=F\times d=mgh\] As you can see velocity does not factor into it.

Answer 2

True, but you would breate harder! Work is energy (calories) so you burn calories twice as fast.

Answer 3

you would be doing the same work while expending more power

Answer 4

Or you could go upstairs in a crate lifted by a crane at different speeds. The work done is the same. Faster just means using more power for less time and comes out at the same work done either way.