Consider an omnidirectional robot with a ring of eight $70KHz$ sonar sensors that are fired sequentially. Your robot is capable of accelerating and decelerating at $50c\frac{m}{s^2}.$ It is moving in a world filled with sonar$-$detectable fixed $($nonmoving$)$ obstacles that can only be detected at $5$ meters and closer. Given the bandwidth of your sonar sensors$,$ compute your robot's appropriate maximum speed to ensure no collisions.