Wunderbar said:
You'll burn the same amount of calories if you walk compared to running the same distance.
It may sound like I'm being argumentative. I apologize if it appears that way. I just wish to make sure we are all accurate.
It still seems that going the same distance, faster, requires more energy, hence more calories. Your body requires more energy to produce the constant acceleration your body requires to keep it's higher speed. If I casually stroll for 10 miles and take 5-7 hours to get there, I will not be very tired, though my feet would hurt. I will have not expended very much energy, at least compared to someone who made it there in <2 hours.
Out of the human anatomical realm, if you drive 100MPH in 5th gear in a given car, for 10 miles, you will expend more fuel than if in said car you drive 35MPH in 5th gear for 10 miles.
The same person running and walking the same distance should burn more calories, expend more energy, running than walking.
Rate x Time = Distance, you must increase the rate to reduce the time by adding energy/acceleration to the item covering distance. Decreasing time takes an increase in energy. Also, if Mass x Acceleration = Force, a guy running has more Force, and if that Force were to hit something, it would transfer more energy. That's because he has more energy. He also has to keep adding more energy to keep up his constant acceleration. The faster his constant acceleration, the more energy.
For the same distance, the faster your rate or more force you carry, the more energy has to be used to keep up the pace.
Now, for the last two paragraphs, I've invoked physics...something I haven't used mathematically in awhile, and only present some basic theories. If I have this all wrong, I would like peeps to show me what I messed up. I'd be willing to listen, cuz I don't think I stumbled upon the equation that would prove this. I just want to make sure we don't confuse anyone who reads this post, tooooo much.
http://www.Fitnessonline.com has some calorie burning forms, to see how many calories you would burn doing "X" exercise for "Y" time at your body weight. It doesn't have anything for "per distance" but you can kinda do the math, if you want. It isn't the best form out there, I'd like to get a link for a better one for ya, but I don't have one for now.
In all this, we still know that doing exercise is much better than NOT doing exercise.