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## Main Question or Discussion Point

I've got a problem, involving non-constant acceleration:

If we fire a spherical bullet horizontally into a watertank, how far will the bullet traverse?

I've figured as much that a spherical bullet provides a retarding force:

[tex]F = -k \cdot v[/tex] where k is a constant.

This should provide the following non-constant acceleration due to Newtons 2nd law.

[tex]a = \frac{F}{m} = - {\frac{k v}{m}}[/tex]

I'm thinking I should integrate two times over a(t) to get an expression for x(t), but since "a" is proportional to v(t) and not directly to t, I dont know how to do it without getting a recursive expression.

If we fire a spherical bullet horizontally into a watertank, how far will the bullet traverse?

I've figured as much that a spherical bullet provides a retarding force:

[tex]F = -k \cdot v[/tex] where k is a constant.

This should provide the following non-constant acceleration due to Newtons 2nd law.

[tex]a = \frac{F}{m} = - {\frac{k v}{m}}[/tex]

I'm thinking I should integrate two times over a(t) to get an expression for x(t), but since "a" is proportional to v(t) and not directly to t, I dont know how to do it without getting a recursive expression.