ok here's the explanation
KE = 1/2 mv^2 , you see when you double velocity you square it and so the kinetic energy goes up by 400% instead of 200%.
For instance, if you are going 10 m/s on a bike and your mass is 50kg then your KE is 1/2* 50kg *(10m/s)^2 = 2500 Newtons of energy.
If you double your velocity to 20 m/s you get: KE = 1/2* 50kg * (20m/s)^2 = 10,000Newtons of force.
Well you can use the same formula almost for resistance, but substitute in resistance for velocity because the same thing happens. When you double velocity , you SQUARE air resistance.
That is why it is so much harder to double your speed when you are riding a bike, because instead of just doubling the air resistance (200% increase in velocity) , you get a 400% increase in resistance.
So just think of it that way. Double velocity and you square Kinetic energy. Double velocity and you also square the air resistance force.
