Answer
$s(t)=1.32(1-e^{-0.606t})$
Work Step by Step
Since, $\dfrac{v_0 m}{k}=1.32$
$s(t)=\dfrac{v_0 m}{k}(1-e^{-(kt/m)} )....(1)$
With the given data, we have:
$\dfrac{(0.80)(49.90)}{k}=1.32$
or, $ k \approx 30.2424$
Equation (1) becomes:
$s(t)=\dfrac{v_0 m}{k}(1-e^{-kt/m} )\\=1.32(1-e^{-(30)t/49.90} ) \\=1.32(1-e^{-0.606t})$
