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

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SUMMARY

The discussion centers on the application of Newton's 2nd Law to determine the speed of an arrow when the force exerted on it is doubled. The initial speed of the arrow is 25 m/s, and the average force is doubled, leading to confusion regarding the resulting speed. The correct speed, when calculated, is 35.4 m/s, demonstrating that while acceleration increases with force, the relationship between force, acceleration, and speed is not linear without considering time. The key takeaway is that doubling the force does not necessarily equate to doubling the final speed due to the influence of acceleration over time.

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  • Understanding of Newton's 2nd Law of Motion
  • Basic knowledge of kinematics and motion equations
  • Familiarity with the concepts of force, mass, and acceleration
  • Ability to manipulate algebraic equations
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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?
 
Physics news on Phys.org
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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