Answer
$$s(t)=0.97(1-e^{-8866t})$$
Work Step by Step
We have: $s(t)=\dfrac{v_0 m}{k}(1-e^{-kt/m} )$
Since, $\dfrac{v_0 m}{k}=0.97$
Plug in the given data; we have: $\dfrac{(0.86)(30.84)}{k}=0.97$
$\implies k \approx 27.343$
Now, $$s(t)=\dfrac{v_0 m}{k}(1-e^{-kt/m} )=0.97(1-e^{-(27.343)t/30.84} )$$
So, $$s(t)=0.97(1-e^{-8866t})$$
