Hello! I hope my post does not breach forum ettiquette, I am new, please, no flaming.

 

I would like to calculate how much energy an object(a horse, for me) expends over a given distance x, at a speed y. I would then like to compare this with energy spent over the same distance x, when accelerating to a maximum speed of y from an initial speed, a.

 

Can anyone help, or at least make sense of my humble request?

 

Tourist.

Ok, you sound like you are looking for change in energy which is work.

 

Ke = .5mv^2

 

ke final - ke initial = work

 

So if you or the horse initial is at rest (0 ke) and at the end of the distance x has reached 10ms the final ke is 50* mass of horse.

 

Meaning the work (joules) or energy expended is 50*mass of horse

 

Now if you throw in different accelerations of the horse over the distance the work doesn't change however the power does.

 

Power depends on time, different accelerations over the same distance will provide different times. P = W/t

 

Hopefully that helps some.

 

However, keep in mind that the classical physics equations are for 'ideal' 'frictionless' situations and even though the equations suggest that it requires no energy for the horse to stay in motion that is obviously not true as it costs energy for it to continue to move its legs in stride.