Calculating Force: The Physics Behind a Rifle's Shot Speed and Barrel Length

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To calculate the force exerted on a bullet in a rifle, the initial speed of 320 m/s and barrel length of 0.82 m are used. The acceleration is determined to be approximately 62,439 m/s². Multiplying this acceleration by the bullet's mass of 0.005 kg yields a force of about 312 N. The discrepancy with the book's answer of 310 N may be due to significant figures. Accurate calculations and attention to significant figures are crucial in physics problems.
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A 5.0 g bullet leaves the muzzle of a rifle with a speed of 320 m/s, What force (assumed constant) is exerted on the bullet while it is traveling down the .82 m long barrel of the rifle?

This is what I have so far. : [.

(320)^2/(2*.82)=t

320/t=a

a= 62439

62439*.005
=312

The back of the book is 310. What did I do wrong?
 
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I got what you got.
 
probably because the book gives answers in significant figures?
 

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