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?