Answer
$s(t)=0.97(1-e^{-8866t})$
Work Step by Step
The distance traveled is: $s(t)=\dfrac{v_0 m}{k}(1-e^{-kt/m} ) ...(1)$
We have: $\dfrac{v_0 m}{k}=0.97$
Now, substitute the given data in the equation (1).
$0.97=\dfrac{(0.86)(30.84)}{k}$
or, $k \approx 27.343$
Equation (1) becomes: $s(t)=\dfrac{v_0 m}{k} \times (1-e^{-kt/m} )=0.97(1-e^{-(27.343)t/30.84} )=0.97(1-e^{-8866t})$$
