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Assume a block of mass 20 kg, initially at rest on a frictionless surface. Suppose at t=0, a force of 10 N is applied. Obviously, the 20 kg mass is supposed to move with a constant velocity which implies that acceleration is 0. Since a force of 10 N is applied, how the acceleration can become 0?
F = ma
10 N = 20kg x a
=> a = 0.5m/s2(how acceleration becomes 0?)

Also, physically, what happens to the applied force? How does it vanish? How long the force is being applied? Or how long the force 10 N will be in picture?

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    $\begingroup$ "Obviously, the 20 kg mass is supposed to move with a constant velocity which implies that acceleration is 0." - I don't see how that follows "obviously" from the statement that a constant force is applied. $\endgroup$
    – ACuriousMind
    Nov 8 '21 at 17:49
  • $\begingroup$ If there's no opposing force (such as no friction, as you mention), when why should the velocity be constant? If you constantly push something with an unbalanced force, it will accelerate and increase in speed. $\endgroup$
    – Steeven
    Nov 8 '21 at 18:07
  • $\begingroup$ A key question (or two) applies: why would you think that a 10 N force on a 20 kg object would produce constant velocity? I suspect you either have an incorrect concept in mind or you have mis-interpreted an observation. $\endgroup$ Nov 8 '21 at 20:29
  • $\begingroup$ Your setup and your question are unclear. $\endgroup$
    – Bill N
    Nov 8 '21 at 23:21
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The force cannot just be applied at the instant $t=0$. It must be applied over some period, from $t=0$ to $t=t_1$, say. While the force is applied, the block accelerates with acceleration $a=0.5$ m/s/s. Once the force is removed the block stops accelerating and continues to move with a constant velocity.

For example, if the force is applied for $10$ seconds, the block will accelerate to $5$ m/s and will then continue to move at this velocity until and unless another force is applied to it.

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Also, physically, what happens to the applied force? How does it vanish? How long the force is being applied? Or how long the force 10 N will be in picture?

Nothing happens to it as long as you apply it. When you stop applying it, then it obviously vanishes.

So the $10\,\mathrm{N}$ force will be 'in the picture' as long as you dictate it to be so.

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how the acceleration can become 0?

The acceleration can only become zero when there is no net external horizontal force acting on the mass, per Newton's second law. Given a frictionless surface and no air resistance, that means it will only become zero when the 10 N force is removed. It will then move with constant velocity of $v=at=0.5$m/s$^2$t per Newton's 1st law, Where $t$ is the duration of the application of the 10 N force.

Hope this helps.

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