There is an object on a smooth horizontal plane. Under the action of horizontal constant force F, it starts to move from static state. After a certain period of time, its speed reaches V, and then after a period of time There is an object on a smooth horizontal plane, which starts to move from rest under the action of horizontal constant force F. after a certain period of time, the velocity reaches V, and then after a period of time, the velocity increases from V to 2V. In these two periods of time, what is the ratio of work done by external force F to the object?

There is an object on a smooth horizontal plane. Under the action of horizontal constant force F, it starts to move from static state. After a certain period of time, its speed reaches V, and then after a period of time There is an object on a smooth horizontal plane, which starts to move from rest under the action of horizontal constant force F. after a certain period of time, the velocity reaches V, and then after a period of time, the velocity increases from V to 2V. In these two periods of time, what is the ratio of work done by external force F to the object?

Because there is no friction, all the work done by F is converted into kinetic energy,
The work done from 0 to V is W1 = m * V * V / 2;
The work done from V to 2V is the total kinetic energy minus W1
w2＝m*2v*2v/2=2m*v*v
So W1: W2 = 1 / 2:2 = 1 / 4