Mechanics Problem Involving Newton's Laws

  1. 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

    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.
  2. jcsd
  3. gabbagabbahey

    gabbagabbahey 5,015
    Homework Helper
    Gold Member

    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?
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