A

To find the distance covered by the scooter under the retardation scenario, we first need to analyze the motion described by the equation of motion under non-constant acceleration.
The deceleration is given by a = -kv, which can be rewritten in terms of velocity: dv/dt = -kv.
This is a separable differential equation. Integrating both sides leads us to:
ln(v) = -kt + C
Rearranging gives us v(t) = e^{-kt + C} = e^{C} e^{-kt} = u e^{-kt} where u is the initial velocity when t = 0.
Now, we substitute v(t) into the formula for distance s(t) = ∫v dt:
s(t) = ∫u e^{-kt} dt = -\frac{u}{k} e^{-kt} + C'
Evaluating this from time 0 to t will give:
s(t) = -\frac{u}{k} (e^{-kt} - 1)
Therefore, the answer simplifies to \frac{u}{k} (1 - e^{-kt}) which corresponds to Option A. The key steps involved separating the variables, finding the integrals, and determining the limits for the bounds of time.