A ball is thrown at a relative velocity of $3 \ m/s$ in $+ve$ $x-$ direction in a rocket in gravity free space. The rocket has a constant acceleration of $2 m/s^2$ also in $+ve$ $x-$ direction.

My question :

Whether uniform acceleration equations of motion would apply in above case when using the rocket as a frame of reference. As an example, would the equation $s= ut + .5at^2$ apply if rocket is taken as frame of reference?

From my understanding the answer should be no since the above equation of motion can only be used when using an inertial frame of reference i.e. when frame of reference is moving at a constant velocity with respect to ground.