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I am not sure how to title this question so apologies if it's inaccurate.

If I throw an object at thrice the escape velocity of earth, what would be its velocity very far away from earth, (at a distance of infinity)?

I tried solving this question by noting that while the velocity (33.6 km/s) is constant, the acceleration is dependent on distance, I don't want to take acceleration as constant.

Acceleration is given by $\frac{GM}{(r+s)^2} ds$ where $s$ is the displacement of the object,

I thought I should integrate this distance dependent acceleration from $0$ to $\infty$ with respect to $s$ but then I get something which isnt a velocity or acceleration?

How do I solve this problem

I am not sure how to title this question so apologies if it's inaccurate.

If I throw an object at thrice the escape velocity of earth, what would be its velocity very far away from earth, (at a distance of infinity)?

I tried solving this question by noting that while the velocity (33.6 km/s) is constant, the acceleration is dependent on distance, I don't want to take acceleration as constant.

Acceleration is given by $\frac{GM}{(r+s)^2}$ where $s$ is the displacement of the object,

I thought I should integrate this distance dependent acceleration from $0$ to $\infty$ with respect to $s$ but then I get something which isnt a velocity or acceleration?

How do I solve this problem