# Forces/Newton's Laws of Motion

This problem really shouldn't be this difficult but for some reason I can't seem to find the answer.

An arrow, starting from rest, leaves the bow with a speed of 26.0 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?

net force= mass x acceleration

Acceleration is unknown in this question. Velocity (I'm assuming it's the final V?) is known (26.0 m/s). Initial velocity is 0. I know that when force doubles, acceleration doubles. That's about as far as I could get.

Doc Al
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I know that when force doubles, acceleration doubles.
Good. What quantity remains the same? When they said "all else remaining the same", what could they have been talking about?

The initial velocity remains the same. But the only other variable that is given is final velocity, which would not stay the same.

Doc Al
Mentor
Hint: The distance the arrow takes to reach the final speed is the same.

How do distance, acceleration, and speed relate?

V^2=Vo^2 + 2ax. But what is x? It isn't known.

Doc Al
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All you want to do is compare the final speeds. You don't need to know the actual distance. Just call it x.

But what is the acceleration?

Doc Al
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But what is the acceleration?
Again, you don't need actual numbers. Call the original acceleration "a". What would be the new acceleration?

It would be 2a

Doc Al
Mentor
It would be 2a
Good. Now solve for the speeds in terms of "a" and "x" and compare. (You can also use ratios.)