Newton's 2nd Law: Doubling Force, Double Speed?

[gxinxing]

Homework Statement

An arrow, starting from rest, leaves the bow with a speed of 25 m/s. If the average force exerted on the arrow would be doubled, all else remains the same, with what speed would the arrow leave the bow?

Homework Equations

force = mass x acceleration

The Attempt at a Solution

Since the mass is constant, I assumed that there's a direct relationship between force and acceleration (in this case, speed, since I believe time is irrelevant) so a doubled force should have resulted in doubled acceleration (50 m/s/time). But the answer is 35.4. Why is that?

 

[ehild]

The acceleration is doubled, but the speed was asked.

ehild

 

[gxinxing]

How do I figure out the speed without a given time?