# What does the equation ${\bf F} = m{\bf a}$ mean in this case?

So I have been studying about momentum and newton's second law. And I was wondering, if an object is traveling in space. If the object has a mass $$m$$ and a velocity $${\bf v}$$ with an acceleration $${\bf a}$$ which is due to some force that causes the body to accelerate and let's say there are no other forces acting on it.

Now $${\bf F} = m{\bf a}$$, so does this mean that the object has potential to exert force when it comes in contact with another object or is it constantly applying force onto space or it tells us about the force which causes its in motion?

• The third one, sort of: it tells about how the motion is changed by the force. This is what you wrote yourself: 'acceleration [..] is due to some force'. The equation tells what acceleration (change of speed) the object gets from the force. Note that speed itself is irrelevant. – Stéphane Rollandin Aug 12 '19 at 8:44
• Related question: Can force be applied without accelerating? – BioPhysicist Aug 12 '19 at 10:49

Newton's second law means that a net force acting on an object causes it to accelerate. It does not mean an object that is accelerating must be exerting a force on something equal to $$F=ma$$. Or explained in a different way, it does not mean that if something is not accelerating that it cannot exert a force. You can easily reason why the latter is false. Right now I'm laying on my bed. My body pushes against the bed, but I'm not accelerating. Therefore, the law does not say my acceleration gives me the capacity to "create" a force.

• “... net force acting on an object causes it to accelerate” — the term causes is probably not very appropriate, as acceleration is not delayed — both force and acceleration begin simultaneously. – MarianD Aug 12 '19 at 13:04
• @MarianD Well good thing I didn't say anything about a delay. I have never heard of the word "causes" to explicitly mean there is a delay. – BioPhysicist Aug 12 '19 at 13:20
• IMHO if one event causes the other one, then it has to be the first in time (definitely not the last ;-)). – MarianD Aug 12 '19 at 13:53
• @MarianD Technically nothing is rigid, so really the force would come before the acceleration of the entire body. In any case, I think this is somewhat of a superfluous point, but thank you for the clarification. – BioPhysicist Aug 12 '19 at 14:56

All that Newton's second law tells us is that acceleration of a particle $$\bf{a}$$ is dependent on the forces acting upon the particle and the particle's mass $$m$$. For a given particle, if the net force $$\bf F$$ is increased, the acceleration is increased.

The most important thing to realize is that this relationship involves not only changes in the magnitude of the momentum or of the velocity but also in their direction.

As you rightly asked, it tells us what is the net force that puts it into motion.

Does this mean that object has potential to exert force when it comes in contact with another object?

Of course, when the objects come into contact, normal forces will be exerted and is not a consequence of this equation. The law gives the dynamical picture of the system under consideration given the net force.

I was in a same situation but after thinking about it I got the answer let me tell you what I understand.

F=Mdv/dt or F=ma let understand theory by an example a car is at rest on a horizontal road, a truck moving with constant velocity v and having mass M strikes the car from back, does the car feel any force, answer is Yes, what is the reason for that force, reason is simple when there is change in momentum of the body it will experience force that what the equation describe F=mdv/dt (m is the mass of car) its initial momentum was zero now it is mv' at the same time change in momentum of truck from Mv to Mv' it also experiences force that is normal reaction

Conclusion wherever there is sudden change in momentum of a body it will apply as well as experience the force, that is what newton third law say, every action there is equal and opposite reaction.