A small rock sinking through water experiences an exponentially decreasing accel

Question

A small rock sinking through water experiences an exponentially decreasing acceleration given by ay(t) = ge-bt, where b is a positive constant that depends on the shape and size of the rock and the physical properties of the water. Based upon this, find expressions for the velocity and position of the rock as functions of time. Assume that its initial position and velocity are both zero and that the +y direction is directly downward. (Use the following as necessary: g, b, and t)
y =
v =               

Explanation / Answer

dv/dt = ay = ge^-bt;

dv = ge^-btdt;

-b*dv = -gd(e^-bt);

-bv = -ge^-bt + g;

v = -g/b + g/be^-bt;

dy/dt = -g/b + g/be^-bt;

dy = (-g/b+g/be^-bt)dt;

y = -gt -(g/b^2)*e^-bt - g/b;

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