# Work, Energy and Power question

1. May 17, 2010

### gaobo9109

1. The problem statement, all variables and given/known data
A cyclist develops constant power when cycling. The air resistance is proportional to the speed of cycling. When he cycles on level ground, the maximum velocity he can attain is v. When he cycles up a slope, his maximum velocity is 1/2v. If he cycles down the same slope, his maximum velocity is av. Ask what is the value of a.

2. Relevant equations

3. The attempt at a solution
The cyclist exerts the same amount of force on the bike at all velocity,thus

On level ground: F = kv2

cycling up a slope: F = 1/4kv2 + mgsinθ
kv2 = 1/4kv2 + mgsinθ
mgsinθ = 3/4kv2

cycling down the slope: kv2 + 3/4kv2 = k(av)2
a2 = 7/4
a = (7/4)1/2

But this is not the correct answer. Can anyone tell me where did I go wrong?

2. May 17, 2010

### PhanthomJay

You assumed that the air resistance was proportional to the square of the speed (kv^2), when it is given that it is proportional to the speed (kv).