Calculate the centripetal acceleration (a_c).

The centripetal acceleration is responsible for changing the direction of the car's velocity and is given by the formula:

$$a_c = \frac{v^2}{r}$$

where $v$ is the speed and $r$ is the radius of the circular path.
Given $v = 60 \text{ m/s}$ and $r = 1200 \text{ m}$:

$$a_c = \frac{(60 \text{ m/s})^2}{1200 \text{ m}}$$ $$a_c = \frac{3600 \text{ m}^2/\text{s}^2}{1200 \text{ m}}$$ $$a_c = 3 \text{ m/s}^2$$

The problem states that the car is increasing its speed at the rate of $4 \text{ m/s}^2$. This is the tangential acceleration, which is responsible for changing the magnitude of the car's speed.

$$a_t = 4 \text{ m/s}^2$$

The centripetal acceleration and the tangential acceleration are perpendicular to each other. Therefore, the magnitude of the total acceleration ($a$) is found using the Pythagorean theorem:

$$a = \sqrt{a_c^2 + a_t^2}$$

Substitute the calculated values:

$$a = \sqrt{(3 \text{ m/s}^2)^2 + (4 \text{ m/s}^2)^2}$$ $$a = \sqrt{9 \text{ m}^2/\text{s}^4 + 16 \text{ m}^2/\text{s}^4}$$ $$a = \sqrt{25 \text{ m}^2/\text{s}^4}$$ $$a = 5 \text{ m/s}^2$$

The acceleration of the car is $\text{5 m/s}^2$.