The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature \( R = 2 \, \text{m} \). Another car approaches him from behind with a uniform speed of \( 90 \, \text{km} / \text{hr} \). When the car is at a distance of \( 24 \, \text{m} \) from his, the magnitude of the acceleration of the image of the car in the side view mirror is \(' a' \). The value of \( 100a \) is ______ \( \text{m} / \text{s}^2 \).
