physics

Without using complicated theories in aerodynamics, the most simple explanation is that when an object moves in air, it has to push sideways the mass of air directly in front of it. In so doing, energy is needed and this energy is deprived from the moving object, the object thus slows down. In other words, the object experiences a resistance force, which is the air resistance. In that sense, a force must be required to keep the object from moving with constant speed.
When the speed of the object increases, the mass of air pushed sideways by the moving object per unit time also increases. More energy is transferred from the object to the air mass. Hence, a larger air resistance force is experienced, and a larger force is requried to balance the increased air resistance to keep the object moving at constant speed.
For example, given an object of volume V m3(=A.L, where A is the cross-sectional area of the object and L is its length), moving with constant speed u m/s, in air of density d kg/m3.
Then in 1 second, the mass of air M pushed sideways by the object is,
M = A.u.d kg/s
Since A and d are fixed, M is proportional to u, the speed of the moving object.
The resistance force experienced is proportional to M, thus it is clear that air resistance is proportional to the speed of the object
Please be aware that the above explanation is only a simplified approach to the real problem. For more exact explanation, especially when turbulence occurs, one should refer to detailed aerodynamic theories.

因為第一個assumption是air resistance是directly proportional to velocity