Using the kinematic equation:
v = vo + at
where v is the final velocity, vo is the initial velocity (which is zero since the cotton ball is dropped), a is the acceleration, and t is the time.
At t = 1.00 s:
v = 0 + (-9.81 m/s²) (1.00 s) = -9.81 m/s
However, there is air resistance acting on the cotton ball, so the acceleration will be less than -9.81 m/s². We don't have enough information to calculate the exact acceleration, but we can eliminate choices A and B because they have an acceleration greater than -9.81 m/s².
For choice C:
v = 0 + (-4.90 m/s²) (1.00 s) = -4.90 m/s
For choice D:
v = 0 + (-4.90 m/s²) (1.00 s) = -4.90 m/s
Therefore, the correct answer is D. v = 2.55 m/s, a = 0.00 m/s².