If an object is at rest ( $\vec{u}=0$)at one reference frame, e.g. with respect to you.
I think you would accept that the NET force acting on the object is zero.

Assume there is another observer which is moving with constant velocity $\vec{v}$ with respect to you.
You saw another observer is moving with velocity $\vec{v}$

Let's back to the previous object, the other observer should find there is no NET force acting on that object.
And that object is moving with $\vec{u'}=-\vec{v}$ with respect to that observer.

From physics point of view: The physics law is the same for all inertia frames, so they all find the same force (or no net force).

An object moving with velocity $\vec{v}$ will be seen as at rest for another observer which is moving at the same velocity $\vec{v}$.

Assume you site in a train which is moving at constant velocity $\vec{v}$ with respect to ground:
For all observer on the ground, you and other people in the train moving with constant velocity $vec{v}$
However, for observer in the same train, all the others are not moving at all ,right? ;)