Bow and arrows, Newtons second law of physics

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Homework Statement

If I have shot an arrow, would that arrow speed slow down due to air resistance? If so, would that mean that the the acceleration would be de-accelerating?

Homework Equations

f = ma

The Attempt at a Solution

This isn't a a homework problem, this is just something I was wondering about the basic laws

Any who, If I shot an arrow where there is air but no gravity, would the arrow eventually slow down? Because i'd imagine if there was no air than the velocity/speed would increase because the acceleration wouldn't change.

Please elaborate fully, this is my first time taking physics, I just want to learn.

 

[Noctisdark]

Once you've shot the arrow, you are no-longer applying some force on it, but the air does ! It's only decelerating by the air resistance, assuming you know calculus
F(air resistance) = -λ(some coefficient)*v(velocity) and you end up with a differential equation whose solution is v(t) = V0 * e(-λt) , speed is falling but at least he have one :)