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When a constant force is applied on body which is free to slide on a surface, does it move with a constant velocity after some time or does the velocity keep on increasing? Please explain it for both cases with and without friction.

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If there is no friction or opposing force, which in your case is not present then the object experiences accelerated motion. This can be easily explained by newton's second law as:

$F=ma$

If there is constant force acting then the body will accelerate that is, the velocity of body keeps on increasing.

In the case where there is friction then there will be an opposing force say $F_{friction}$ which will oppose the motion of the object as follows:

$F-F_{friction}=ma$

Now for the object to move with a constant velocity, the quantity $F-F_{friction}$ which is the net force on the body should be equal to $0$ which means

$ma = 0$

Hence no acceleration = constant velocity

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Without friction;

As the Newtonian Laws state that F=m*a, which means under constant force a body of mass will always accelerate no matter what. So no, it will not reach a constant velocity unless the Net Force is zero. In a world without friction (no friction, skin drag, or surface drag etc.) then net force will equal to the constant force applied, given there are no other acting forces.

With friction;

It is the same principle as without friction. As long as Net Force is greater than 0, the body of mass will always accelerate. In real world with friction, we usually see that, even though Constant Force>Friction Force, at higher velocities, drag force comes in the play. Which eventually makes the Net Force zero.

All in all, as long as your NET Force is greater than Zero, your body of mass will always accelarate in accordance with Newtonian Laws. If you are asking if the speed can surpass the speed of light given enough time, that is a NO since, under relativistic conditions different laws of physics are applied.

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  • $\begingroup$ You should possibly add that drag forces scale with the object velocity (either as $v$ or $v^2$) and this is the reason they outweight the external force at some point. $\endgroup$
    – svavil
    Mar 9, 2016 at 11:09
  • $\begingroup$ @svavil Yes you are right, when I was writing the answer though about including it, however given the triviality of the question, decided to left it out. Since, there are much more forces in play, when the speed gets larger. $\endgroup$ Mar 9, 2016 at 11:12
  • $\begingroup$ Is it possible to make a body slide at a constant velocity considering friction and drag forces? $\endgroup$
    – SS4
    Mar 9, 2016 at 11:21
  • $\begingroup$ Yes, it is possible. When the Net force equals zero, object will go at constant velocity. Which means ForceInput - FrictionForce - DragForce = 0 However constant velocity also means a velocity of zero as well. Basically with NetForce zero you will have Velocity=InitialVelocity $\endgroup$ Mar 9, 2016 at 11:23
  • $\begingroup$ @SS4 Yes as i answered , if the net force on the body is zero then there is no acceleration and hence the body will move with constant velocity. $\endgroup$
    – hxri
    Mar 9, 2016 at 11:23

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