A

Step 1: Calculate the maximum possible speed before skidding using the formula for frictional force. The frictional force is given by $F_f = \\mu \\cdot mg = 0.2 \\cdot m \\cdot g$. This frictional force provides the necessary centripetal force for circular motion, which can be given by $F_c = \frac{mv^2}{R}$.
Step 2: Setting these equal, we have:
$$0.2 \\cdot mg = \\frac{mv^2}{R}$$
which simplifies to:
$$v^2 = 0.2gR$$
Step 3: Now, noting that $a = 1 \, m/s^2$ and the car accelerates from rest, we use the equation of motion $v = u + at$, where $u = 0$. Hence:
$$v = 1 \, t$$
Substituting $v$ in the previous equation gives:
$$(1 \, t)^2 = 0.2gR$$
Step 4: Solve for time $t$. This yields:
$$t^2 = 0.2gR$$ and thus
$$t = \sqrt{0.2gR}$$
Finally, substituting the values of $g = 9.8 \, m/s^2$ and $R$ as given provides the required time to skidding.