# A little problem of understanding the connection between kinetic energy and work $W=\Delta E_{kin}$

I am a little stucked in understanding the connection between kinetic energy and work $W=\Delta E_{kin}$.

This is a second to second thing so:

Let's say someone is pulling a box. The box is at rest when he starts and comes to rest when he stops to pull. If I would then investigate this process I would come to the conclusion that it has no kinetic energy (v at the beginning and at the end ist equal 0). And as you can see - it is at rest so the statement "is there".

Question (1): Does this count as work done ? Since $W=\Delta E_{kin}$ there is no work done, isn't it ?

But (!) If you cut out this little tiny interval where the box stops and rests and only look on the interval in which it actually moves:

While we move the box we are doing work on it and while it moves it has a certain amount of kinetic energy.

Is that correct?

Sorry if this may sound rediculously easy but I am yet a little confused

3. So this is what is happening. On a frictionless ideal surface, you would push an object and it would acquire a kinetic energy given by $E_k=\Delta W$, so it would get the speed $v=\sqrt{\frac{2W}{m}}$.