# Why does objects with zero acceleraton move?

My question is, if we apply a force on an object to move it with a constant velocity, of course it will move. But what I don't understand is, why will it move? From Newton's law F=ma and in this case a=0 then F=0. So if F equals zero and that doesn't match the reality. I'm confused.

• Your mistake is in the sentence "if we apply a force on an object to move it with a constant velocity". If we apply a force (ignoring friction, say in a vacuum), the object willnot move with constant velocity. Instead, it will accelerate. If f=0, then acceleration=0, i.e. speed is constant. – hdhondt Nov 24 '14 at 10:10

There does not need to be a force on an object for it to move, only for it to accelerate, as can be seen from Newton's second law:

$$F=m \cdot a$$

I think your confusion arises from forgetting to take into account frictional forces. In practice, a moving object will slow down because of friction: the net force is not zero! Therefore you need to apply an external force to the object to keep it moving.

$$F_{external} - F_{friction} = F = m \cdot a = 0$$

If this external force is equal but opposite to the friction, Newton's second law correctly shows that the acceleration is zero:

$$F_{external} - F_{friction} = 0 \rightarrow F=0\rightarrow a = 0$$

• let's say i'm moving a box which is on a table with an external force that's making the box move with a constant velocity, and there is a friction force. Does that mean F external - F friction = m.a , and a=0 then F external - F friction = 0 ? – ALz Nov 12 '14 at 9:38
• forgot to mention (and i continued applying the external force to make the box move with a constant velocity) – ALz Nov 12 '14 at 9:47
• yes, exactly, that is correct! – Oebele Nov 12 '14 at 11:18
• one more question :) , but in this case F external = F friction and from this equation i understand that the box won't move and that's inconsistent with what's happening, which is the box is moving. – ALz Nov 12 '14 at 12:15
• To make sure the box starts moving, $F_{external}$ must be greater than $F_{friction}$ such that $a>0$ such that the box starts moving. Once it is in motion, the external force can be reduced to the same magnitude as the frictional forces, such that $a=0$ and therefore the speed of the box is constant. – Oebele Nov 12 '14 at 12:24

First Newton law: When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.

What this means is that if you have an object at rest, you need a force to make it move. Once you stop the force the object will keep moving at a constant speed, so its acceleration and the net force upon it will be zero. I think your confusion is that you believe that you need a force to keep an object moving at constant speed and that the object will stop if you do not keep doing a force upon it. That is wrong, but do not worry, even Aristotle believed that.

• sorry maybe i haven't clearly clarified what i'm not understanding But let's say i'm moving a box which is on a table with an external force that's making the box move with a constant velocity and i continued applying the external force to make the box move with a constant velocity, and there is a friction force. Does that mean F external - F friction = m.a , and a=0 then F external - F friction = 0 ? – ALz Nov 12 '14 at 9:52
• yes, if the velocity is constant the friction must be equal in magnitude but opposite in sign to the force, otherwise the box would accelerate. – Wolphram jonny Nov 12 '14 at 10:06
• so if ΣF = 0, that doesn't mean the box is not moving ? I thought if ΣF for an object = 0 that means the object is not moving. – ALz Nov 12 '14 at 10:15
• exactly, it doesn't mean the box is not moving. It can be moving at constant speed. If no force tries to slow the object, it will keep moving forever (no forces needed for that). You only need a net force to change its speed. Such as from zero to 1m/s. Then you stop the force and the object will keep moving at that speed. But that would happen in space, here on earth you have friction everywhere (even from air), so all objects will eventually stop, but due to tiny frictional forces. – Wolphram jonny Nov 12 '14 at 10:47

That is because when you apply force on any object momentum is transferred which means velocity is transferred to an object at rest. now we know rate of change of velocity is proportional to force applied so if velocity does not change, so rate of change of momentum is zero and so force applied is also zero and hence the object will continue to move. however if there is some opposing force ex. Friction velocity slows and object also stops reason being rate of change of momentum is now negative and force that is applies is now opposite to velocity (Consider object moving up gravitational pull is opposite to velocity) and so it has stopping effect.

The second law states that the net force on an object (F) is equal to the rate of change (that is, the derivative with respect to time) of its linear momentum p (p = m*v, where v is the velocity) in an inertial reference frame.

When F is zero, due to the above equality, dp/dt is also zero. This means that d(mv)/dt = 0 --> mv = const --> v = const. Therefore, the body will move with constant velocity.