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When a body has a net force of 0 on it, one cannot say that it is at rest or in motion at a constant velocity.

If a body is accelerating because of some force and I want to stop it, I can apply the same force in the opposite direction. Unfortunately, that seems to mean that the body will start moving at the velocity it had when the opposite force was applied.

Does this mean that you cannot ever stop a body (generally, but specifically when the body has a constant acceleration) by applying an equal and opposite force?

How then do you stop such a body? You have to apply a force that keeps increasing in amount until the body comes to rest?

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  • $\begingroup$ You must apply desired force for desired time, bring the body to rest or whatever velocity you want and then stop the acceleration , but fixed acceleration is not going to get a moving body to stop as it would ultimately start travelling in opposite direction. $\endgroup$
    – Rijul Gupta
    Commented Oct 26, 2013 at 20:51
  • $\begingroup$ @Sancho ""When a body has a net force of 0 on it, one cannot say that it is at rest or in motion at a constant velocity" - This isn't true" --and why is that? $\endgroup$
    – meonstackexchange
    Commented Oct 26, 2013 at 21:58
  • $\begingroup$ @Sancho He just said that the momentum is constant, which implies either the velocity is 0, or the velocity is not changing. I would think that if a body has 0 velocity it is in rest, and if not it is in motion. Where did I go wrong? $\endgroup$
    – meonstackexchange
    Commented Oct 26, 2013 at 23:42

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Suppose you have an object accelerating due to a force $F$. Then, you apply the same force in opposite direction, $-F$. There is no net force, so obeying Newton's first law it will move at constant velocity. So the answer to your first question is yes.

As you guessed, you should apply an additional force to stop it. Of course, you must apply this force only until it stops.

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  • $\begingroup$ I guess the summary is that you have to have a force that counters the existing force on the body + force that is required to change velocity from the current velocity to 0 in the desired time or Frequired = Fcurrent + v/t where v is the current velocity and t is the time in which you want to stop the body. The quicker the time, the higher the required force. $\endgroup$
    – pran
    Commented Oct 26, 2013 at 21:15
  • $\begingroup$ The applied force could be $F=-F_0-mv/t$, but this if you want constant acceleration. In general, the force could have any form. $\endgroup$
    – jinawee
    Commented Oct 26, 2013 at 21:18
  • $\begingroup$ You are right. I was only talking about constant acceleration and accidentally missed the m in my equation. In reality, any higher force in any form would result in a deceleration that would lead to the body stopping after a while. $\endgroup$
    – pran
    Commented Nov 1, 2013 at 4:28
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First, let's clear up a misstatement in the first sentence of your question. To say that a particle has zero net force acting on it is to say that the particle's momentum is constant:

$\vec F = \dfrac{d\vec p}{dt} = 0 \rightarrow \vec p$ is constant

Now, to your question:

How then do you stop such a body? You have to apply a force that keeps increasing in amount until the body comes to rest?

If wish to reduce the momentum to zero, you must apply a net force in the opposite direction of the momentum.

In your example, all that is required is for you to apply larger force in the opposite direction of the other force and it will need to be time varying since, at the moment the particle stops, you must reduce your force to be equal to the other force.

However, it need not vary until the particle stops. In other words, your force could be constant until the particle stops at which point your force would instantly change to a smaller, constant force.

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