First, let us go back to the time when this formula was devised. We knew that an object can be pushed and it can have different magnitudes. Now, the basic problem arose, how to measure this push or the force?

Newton found out that as the force was varied so did the acceleration of an object of mass say $m$. Further, as the force was doubled the acceleration also got doubled for that stationary object (don't confuse yourself with the reference frame, take any inertial frame. An earth can act as an inertial frame to a good approximation). So, acceleration is directly proportional to the applied force. Newton tried to relate this force to the acceleration of the object or you can say the applied force to rate of change in momentum of the object but, if one relate it vice versa, one may go wrong because acceleration is directly dependent on the applied force and not the applied force is directly dependent on the acceleration of the given object of mass $m$

In simple words acceleration is dependent on the applied force but it dosen't makes much sense to say that the applied force is directly dependent on the acceleration of the given object. In your case acceleration was hindered but it dosen't mean that the force wasn't applied.

First, let us go back to the time when this formula was devised. We knew that an object can be pushed and it can have different magnitudes. Now, the basic problem arose, how to measure this push or the force?

Newton found out that as the force was varied so did the acceleration of an object of mass say $m$. Further, as the force was doubled the acceleration also got doubled for that stationary object (don't confuse yourself with the reference frame, take any inertial frame. An earth can act as an inertial frame to a good approximation). So, acceleration is directly proportional to the applied force. Newton tried to relate this force to the acceleration of the object or you can say the applied force to rate of change in momentum of the object but, if one relate it vice versa, one may go wrong because acceleration is directly dependent on the applied force and not the applied force is directly dependent on the acceleration of the given object of mass $m$

In simple words acceleration is dependent on the applied force but it dosen't makes much sense to say that the applied force is directly dependent on the acceleration of the given object. In your case acceleration was hindered by an equal and opposite force but it dosen't mean that the force wasn't applied.

First, let us go back to the time when this formula was devised. We knew that an object can be pushed and it can have different magnitudes. Now, the basic problem arose, how to measure this push or the force? Newton found out that as the force was varied so did the acceleration of an object of mass say $m$. Further, as the force was doubled the acceleration also got doubled for that stationary object (don't confuse yourself with the reference frame, take any inertial frame. An earth can act as an inertial frame to a good approximation). So, acceleration is directly proportional to the applied force. Newton tried to relate this force to the acceleration of the object or you can say the applied force to rate of change in momentum of the object but, if one relate it vice versa, one may go wrong because acceleration is directly dependent on applied force and not applied force is directly dependent on the acceleration for a given object of mass $m$

In simple words acceleration is dependent on the applied force but it dosen't makes much sense to say that the ** applied force** is dependent on the acceleration of the given object. In your case acceleration was hindered but it dosen't mean that the force wasn't applied.

First, let us go back to the time when this formula was devised. We knew that an object can be pushed and it can have different magnitudes. Now, the basic problem arose, how to measure this push or the force? 

Newton found out that as the force was varied so did the acceleration of an object of mass say $m$. Further, as the force was doubled the acceleration also got doubled for that stationary object (don't confuse yourself with the reference frame, take any inertial frame. An earth can act as an inertial frame to a good approximation). So, acceleration is directly proportional to the applied force. Newton tried to relate this force to the acceleration of the object or you can say the applied force to rate of change in momentum of the object but, if one relate it vice versa, one may go wrong because acceleration is directly dependent on the applied force and not the applied force is directly dependent on the acceleration of the given object of mass $m$

In simple words acceleration is dependent on the applied force but it dosen't makes much sense to say that the applied force is directly dependent on the acceleration of the given object. In your case acceleration was hindered but it dosen't mean that the force wasn't applied.