While deriving the second equation of motion , How do we know that we r moving in a straight line? 

Dear student,

While deriving the second equation of motion, we consider the particle to start with initial velocity u, and moves under a constant force F =ma. So that the magnitude of the velocity changes.
And as the force is considered to be constant, then the acceleration is also constant. Thus the change in velocity has a linear relation with time;
as $v=u+at$
that's why while deriving second equation of motion, we consider the simple situation that the body is moving in a staright line.
Regards,