C

Step 1: Identify the types of acceleration
In circular motion, a body experiences two types of acceleration:
1. Centripetal Acceleration (a_c): This is due to the change in direction of the velocity vector and is given by the formula:
$$a_c = \frac{v^2}{r}$$
where v is the linear speed and r is the radius of the circular path.

2. Tangential Acceleration (a_t): This is due to the change in the magnitude of the velocity vector (speeding up or slowing down). It is given as the rate of change of speed.

Step 2: Calculate Centripetal Acceleration
Given:
Speed, v = 30 m/s
Radius, r = 500 m
Use the formula for centripetal acceleration:
$$a_c = \frac{(30 \text{ m/s})^2}{500 \text{ m}} = \frac{900}{500} = 1.8 \text{ m/s}^2$$

Step 3: Identify Tangential Acceleration
Given tangential acceleration, a_t = 2 m/s².

Step 4: Calculate the Total Acceleration
The total acceleration a is the vector sum of the centripetal and tangential accelerations. We can find the magnitude of this resultant acceleration using the Pythagorean theorem:
$$a = \sqrt{a_c^2 + a_t^2}$$
Substituting the values:
$$a = \sqrt{(1.8)^2 + (2)^2} = \sqrt{3.24 + 4} = \sqrt{7.24} \approx 2.69 \text{ m/s}^2$$

Step 5: Result
The acceleration of the car at that moment is approximately 2.69 m/s².