If a force of 15 n is applied to an object with a mass of 7 kg, the object will accelerate at m/s^2

what will it accelerate to ?

Newton's 2nd law:   

                   Force = (mass) x (acceleration)

                   (15N)  =  (7 kg) x (acceleration)

Divide each side
by  7kg :
                   (15 N) / (7 kg)  =  acceleration

                   acceleration  =  (15/7)  m/s²

                                           =   2.143... m/s²          (rounded)

As long as the force continues pushing it the object,
it'll continue moving about 2.143... m/s faster every
second.   No limit.

Well, yes, I'll admit that the numbers WILL start changing
when it reaches a significant fraction of light-speed.  If the
object never runs into anything, then it'll reach, say, 30% of
light speed after about  13 years at that rate of acceleration.