We can start by finding the magnitude of the automobile's centripetal acceleration using the formula:
a = v^2 / r
where v is the instantaneous speed of the automobile and r is the radius of the circular road. Plugging in the given values, we get:
a = (4 m/s)^2 / 20 m = 0.8 m/s^2
The centripetal acceleration is related to the angular acceleration by the formula:
a = r * alpha
where alpha is the angular acceleration. Solving for alpha, we get:
alpha = a / r = 0.8 m/s^2 / 20 m = 0.04 rad/s^2
Therefore, the automobile's angular acceleration is 0.04 rad/s^2 when its instantaneous speed is 4 m/s.