Chapter 9: First-Order Differential Equations - Section 9.3 - Applications - Exercises 9.3 - Page 543: 3

$$s(t)=4.91(1-e^{-\frac{(22.36)}{39.92}t} )$$

We have: $s(t)=\dfrac{v_0 m}{k}(1-e^{-kt/m} )$ Since, $\dfrac{v_0 m}{k}=4.91$ Plug in the given data; we have: $\dfrac{(275)(39.92)}{k}=4.91$ $\implies k \approx 22.36$ Now, $$s(t)=\dfrac{v_0 m}{k}(1-e^{-kt/m} )=4.91(1-e^{-(22.36)t/39.92} )$$ So, $$s(t)=4.91(1-e^{-\frac{(22.36)}{39.92}t} )$$