A person fishing hooks a 3.0-kg fish on a line that can only sustain a maximum of 35 N of force before breaking. At one point while reeling in the bass, it fights back with a force of 45 N. What is the minimum acceleration with which you must play out the line during this time in order to keep the line from breaking?

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To find the minimum acceleration with which you must play out the line to keep it from breaking, we need to consider Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the fish is exerting a force of 45 N, while the line can only sustain a maximum force of 35 N.

Let's assume that the force exerted by the fish is in the positive direction (towards the person fishing), while the direction of acceleration is in the negative direction (away from the person fishing). Therefore, the net force on the line is given by:

Net force = Force exerted by the fish - Maximum force the line can sustain

In this case, the net force on the line would be:

Net force = 45 N - 35 N
Net force = 10 N

We know that the net force acting on the line is equal to the mass of the fish multiplied by its acceleration. Rearranging the formula gives us:

Acceleration = Net force / Mass

Given that the mass of the fish is 3.0 kg, we can substitute the values into the formula to solve for acceleration:

Acceleration = 10 N / 3.0 kg
Acceleration ≈ 3.33 m/s²

Therefore, the minimum acceleration with which you must play out the line during this time is approximately 3.33 m/s² to keep the line from breaking.