# Will something accelerate forever if a constant force is applied on a frictionless plane?

Will something accelerate forever if a constant force is applied on a frictionless plane, or will it continue to move with constant velocity the moment the applied force is removed?

• why would it not continue to accelerate? this is newtons laws of motion – Alex Robinson Feb 26 '18 at 11:56
• As it's a frictionless plane , the $something$ will move with constant velocity as soon as force is removed ... – user182687 Feb 26 '18 at 11:57
• @sithuhlaing... Answer it , what will be the work done by you when $something$ moves incessantly ...? – user182687 Feb 26 '18 at 11:59
• Infinity, of course. but if only if I keep applying the force, right? – sithuhlaing Feb 26 '18 at 12:01
• @sithuhlaing...infinite it is till you apply force up to infinity ... Or else not ... – user182687 Feb 26 '18 at 12:03

## 3 Answers

It will continue to accelerate for as long as the force is applied. If it is applied forever it will accelerate forever, however if the force ever stops, the object will move at a constant velocity.

• Perhaps change "if it ever stops" to "if the force ever stops" as "it" is potentially ambiguous. – StephenG Feb 26 '18 at 13:07

I) Circular motion

If circular motion is allowed in your question, then, you need to prove, at least, that: the universe, it’s laws and mater (any gravitational source) are eternal.

In this framework a moon made up of eternal matter orbiting a planet made up with similar (eternal) stuff, in a perfect circular orbit will be under constant acceleration forever.

II) Linear motion

In this case you should not only prove that the universe, it’s laws and mater (any gravitational source) are eternal, but that it is infinite in size and has an infinite net energy in it as well, because

Under constant linear acceleration (force)

1. the displacement is $x=\frac{1}{2}at^2$, and speed $v=at$, therefore if $t \rightarrow \infty$ then $x \rightarrow \infty; \, v \rightarrow \infty$.

2. the work done is $W=max= \frac{1}{2}m(at)^2$, therefore if $t \rightarrow \infty$ then $W \rightarrow \infty$.

*) $a$: Magnitude of acceleration; $t$: time elapsed; $m$: body mass.

PS: This is under Newtonian approach, at some moment relativistic effects are going to be impossible ignored anymore. In this case your infinity will just be the speed of light $c$ and the results will be: $t \rightarrow \infty$ then $x \rightarrow \infty; \, v \rightarrow c; \, W \rightarrow \infty$.

Assuming you are talking about linear motion, NO, it won't. As the speed of the mass keeps on increasing and becomes comparable to the speed of light, the relativistic mass of the particle starts to play a role, $m=\frac{m_o}{\sqrt{1-\frac{v^2}{c^2}}}$ where $m_o$ is the rest mass of the particle. You see once this becomes "$infinite$" (very large) for any further acceleration, either you have to increase the amount of force that you are applying or with the same force and increasing mass the acceleration would keep on decreasing. So once the speed is quite close to the speed of light (say $0.99999c$), you need infinitely large force to further accelerate it; and this is something which is very non physical (at least to me).