The correct answer is A. 2 m/s^2.
The acceleration of an object is the rate at which its velocity changes. It is measured in meters per second squared (m/s^2). The formula for acceleration is $a = \frac{F}{m}$, where $F$ is the force in Newtons (N) and $m$ is the mass in kilograms (kg).
In this case, the force is 200 N and the mass is 100 kg. Substituting these values into the formula, we get $a = \frac{200 \text{ N}}{100 \text{ kg}} = 2 \text{ m/s}^2$.
Therefore, the acceleration of the object is 2 m/s^2.
Option B is incorrect because it is the mass of the object, not the acceleration.
Option C is incorrect because it is the square of the acceleration, not the acceleration itself.
Option D is incorrect because it is the time it takes for the object to accelerate, not the acceleration itself.