4. A track runner runs at constant speed around a circular track.If the runner is 85.6 meters from the track's center and has a tangential speed of 20m/s what is the centripetal acceleration?

The centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is always directed towards the center of the circle. The formula for centripetal acceleration is given by a = v^2 / r, where v is the tangential speed and r is the radius of the circular path. In this case, the runner is 85.6 meters from the track's center, which is the radius of the circular path. The runner's tangential speed is 20 m/s. Substituting these values into the formula, we get a = (20 m/s)^2 / 85.6 m = 4.65 m/s^2. Therefore, the centripetal acceleration of the runner is 4.65 m/s^2.