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

AI Thread Summary
Doubling the force applied to the arrow increases its acceleration, but it does not directly double the final speed due to the relationship between acceleration, time, and distance. The key equation to consider is that acceleration is the change in velocity over time, and without a specified time frame, the final speed cannot be simply calculated by doubling the initial speed. The discussion highlights the importance of understanding the kinematic equations that relate acceleration, time, and distance to determine final speed. The confusion arises from assuming a linear relationship between force and speed without considering the effects of time and distance traveled. Thus, the final speed of the arrow, when force is doubled, is 35.4 m/s, illustrating the complexities of motion under varying forces.
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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?
 
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The acceleration is doubled, but the speed was asked.

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