Why is it easier for a plane to accelerate when taking off?

Answer 1

Because the force opposing the forward acceleration of the aircraft is drag, and drag is proportional to the square of the relative velocity. So when the airplane is accelerating from standing still, at first there is almost no drag force to oppose the acceleration. As the airplane increases its speed, however, the drag force increases rapidly. In steady flight, the drag force is exactly equal to the force being produced by the propeller.