A cylindrical drum, pushed along by a board rolls forward on the ground. There is no slipping at any contact. The distance moved by the man who is pushing the board, when axis of the cylinder covers a distance L will be

Let v0 be the linear speed of the axis of the cylinder and ω be its angular speed about the axis. As it does not slip on the ground hence ω = v0R. Where R is the radius of the cylinder.  Speed of the topmost point is v = v0+ωR = 2v0Since time taken by the axis to move a distance L is equal to t = Lv0.In the same interval of time distance moved by the topmost point is S = 2v0×Lv0 = 2L