B

Step 1: Identify the radial acceleration (centripetal acceleration) and tangential acceleration.
The radial acceleration at any point in circular motion is given by \( a_r = \frac{v^2}{r} \), where \( v \) is the speed and \( r \) is the radius.
Step 2: Determine the linear speed at \( t = 2 \) seconds. Since the particle starts from rest and accelerates at a constant rate of \( 2 \, \text{m/s}^2 \), we can find the speed using the equation \( v = a t = 2 \times 2 = 4 \, \text{m/s} \).
Step 3: Calculate the radial acceleration: \( a_r = \frac{v^2}{r} = \frac{(4)^2}{1} = 16 \, \text{m/s}^2 \).
Step 4: The tangential acceleration \( a_t \) is the rate of increase of speed, which is given as \( 2 \, \text{m/s}^2 \).
Step 5: The net acceleration is the vector sum of radial and tangential accelerations given by \( a = \sqrt{a_r^2 + a_t^2} = \sqrt{16^2 + 2^2} = \sqrt{256 + 4} = \sqrt{260} = 16.12 \, \text{m/s}^2 \).
Since the net acceleration is provided in the question as \( N \, \text{m/s}^2 \), we conclude \( N = 16.12 \). Therefore, the answer is B.