newtonian mechanics - Stone thrown in empty space

This is a supplementary question to What happens if object is thrown in empty space?

Via the following logic:

$$E = \frac{(mv)v}{2}\\ E = \frac{pv}{2}\\ \Delta E = \Delta p\times \Delta \frac{v}{2}\\ \Delta p = m\times \Delta v \\ \Delta p = ma\\ \Delta p = F\\ \Delta E = F \times \Delta \frac{v}{2}$$

Just when an object leaves our hand, the energy gets stored as Kinetic Energy, which can be represented as $\frac12 mv^2$. If we say that there was an initial kinetic energy and calculate the change in that, then $\Delta E$ gets related to $F$. If there is a force then there is acceleration as well, which means there should be acceleration in object.

Is the above logic correct? If not, why?