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So, when biking, I noticed that when going up hills, it was less tiring if I went up them more quickly. This is not total Work done as is Force * Distance, as that should be the same.

But the longer one is going uphill, the longer gravity is pulling you backwards. And if you only are providing enough force to counteract the force of gravity (from a stop), you will not make it up the hill, yet you will feel quite tired afterwards. While if one pushes really hard, then one will hardly slow down at all.

I know that if you are coasting, then the conservation of energy applies, and $v_i^2 = v_f^2 + C$ where C is the gravitational potential energy at the top of the hill. But this doesn't explain why it is more taxing to go up a hill slowly than quickly. It's the same amount of energy transformed into gravitational potential anyways.

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It's complicated to mix physics objects like force and work with concepts like "tiring" and biomechanics. –  Diego Mar 13 '11 at 15:01
    
    
Dear @Tyr, I think that you're boasting that you can go up the hill quickly. If the slope is significant and my speed is more than 10-15 kilometers per hour, I may end up totally exhausted! ;-) Obviously, your rule that higher speed means less exhaustion isn't universal. :-) Otherwise I agree that some energy may be uselessly wasted just by preserving the position - except that I don't think it's the case of biking. –  Luboš Motl Mar 13 '11 at 17:36
    
There is also the issue as to whether this has anything to do with the gearing on the bike. –  Roy Simpson Mar 13 '11 at 18:27

2 Answers 2

When your going up a hill at a high rate of speed chances are that you started on a horizontal surface going at a high speed and made your way up the hill at a quicker rate so while you are actually going up the hill you are useing the momentum that you got from the above mentioned horizontal surface so it definitely is easier.

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In can help to consider power, the rate of energy use which is not the same in your two cases. This can lead to an understanding of how the same total energy use can result in different levels of 'tiredness'. But as above you also need to take into account biomechanics and recovery time to properly understand the physiological effects.

Can I suggest in direct answer that you are more physically suited to sprinting than endurance physical events, this can be explained best by biologists!

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