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let's imagine an object at rest in a frictionless surface (ignore air resistance too!) how can we make it move at a constant velocity? we need force right? If force is applied wouldn't it accelerate indefinitely?

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let's imagine an object at rest in a frictionless surface(ignore air resistance too!) how can we make it move at a constant velocity?

You first need to apply a net force to accelerate the object, per Newton's second law. Then when the object reaches a desired velocity, you remove the force and the object continues on at that constant velocity. That's because there is no opposing friction force, so once the applied force is removed, the net force of zero and the velocity remains constant per Newton's first law.

If force is applied wouldn't it accelerate indefinitely?

As long as the force continues to be applied, the object will continue to accelerate. (Then, theoretically, the only limitation on its acceleration is the object cannot reach the speed of light).

Hope this helps.

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You can always remove force as soon as it reaches desired amount of speed.

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If force is applied wouldn't it accelerate indefinitely?

Only if force is applied indefinitely and only up until near the speed of light. It only accelerates while force is applied. Don't forget about mass and inertia which prevents infinite instantaneous acceleration when a non-zero force is applied.

Once the force is removed, since there is no friction, what remains in motion stays in motion at constant velocity.

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Case 1 - No force Applied

If object is moving in a friction less surface with a constant velocity, Acceleration is the change of velocity per unit time, so if there is no force, all we know is that the acceleration is zero. Therefore, the velocity is not changing. If the object was already moving, then it will just keep moving. So, yes, the object can be moving when there is no force applied to it.

Case 2 - Force Applied

The basic idea and formulas

The force of friction depends on two factors: the coefficient of friction and the normal force. For any two surfaces that are in contact with one another, the coefficient of friction is a constant that depends on the nature of the surfaces. The normal force is the force exerted by a surface that pushes on an object in response to gravity pulling the object down. In equation form, the force of friction is

f=μN, where μ is the coefficient of friction and N is the normal force.

As far as reality,μ can never be 0. The permeability of free space, μ0, is a physical constant used often in electromagnetism. It is defined to have the exact value of 4π x 10-7 N/A2 (newtons per ampere squared).

It is connected to the energy stored in a magnetic field,.

μ0 is no longer a defined constant (per the former ... The parameter μ0 is a measurement-system constant, not a physical constant that can be measured.

References

https://en.wikipedia.org/wiki/Vacuum_permeability

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    $\begingroup$ You are conflating the coefficient of friction with the permeability of free space . They might have same symbols but they are completely different. Please change your answer $\endgroup$ Apr 25 at 19:21

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