Two cars go round a large, flat roundabout, both anticlockwise, on circular lanes with the same centre O. Car A is on the inner lane, of radius $30\ \text{m}$, at a steady $15\ \text{m/s}$. Car B is on the outer lane, of radius $40\ \text{m}$, at a steady $20\ \text{m/s}$. At one instant O, A and B lie on one straight line, with A between O and B, as shown in the figure. At that instant, what is the acceleration of B relative to A (as measured by an observer who moves with A but does not turn)?

Fig. 1: Top view of a roundabout: two circles with the same centre O, of radius 30 m and 40 m. Car A is on the inner circle and car B on the outer one, on the same straight line from O, with A between O and B. Both move anticlockwise: A at 15 m/s and B at 20 m/s.