Mechanics Problem Involving Newton's Laws

OpticalFreeze

1. The problem statement, all variables and given/known data
An arrow, starting from rest, leaves the bow with a speed of 19.5 m/s. If the average force exerted on the arrow by the bow were doubled, all else remaining the same, with what speed would the arrow leave the bow?




2. Relevant equations
f=ma


3. The attempt at a solution
I know that when the force is doubled, so is the acceleration and therefore the rate of change in velocity is increased. I know that the velocity is not simply doubled as the acceleration increases the velocity over time. I'm not sure where to go with this problem because every possible solution I can think of would involve me knowing the time or the displacement, which I can't figure out how to get from the problem.

Any help would be greatly appreciated.

gabbagabbahey

I think that the key phrase in the question is "all else being the same" So if the acceleration before doubling was calculated using a time interval T , you would use the same interval T in calculating the acceleration after the force is doubled. If T stays the same and a is doubled, what must happen to v?