First of all, both the object and the rope are subjected to F force, and there is no friction resistance, so it is necessary to do uniform and accelerated linear motion. According to the second law of cattle:

F==(m+m')*a

The acceleration of the solution is a = = F/(m+m')

Then take a point at will. The distance m' from the point to the object is x, and the linear density is constant m/l because the linear mass distribution is uniform. At this time, put on Zhang Liwei T.

Now consider the X-length rope and the object as a whole, so the pulling force T is the motive force of the whole movement.

t = =(x * m/l+m ')* a = =(x * m/l+m ')* F/(m+m ')