Final answer:
The centripetal acceleration of the cyclist is 0.225 m/s², calculated using the formula a_c = v^2 / r with the given speed and radius of the bend.
Step-by-step explanation:
The centripetal acceleration of the cyclist can be calculated using the formula for centripetal acceleration: a_c = v^2 / r, where v is the linear velocity and r is the radius of the circular path. Plugging the given values into the formula, we get a_c = (3.0 m/s)^2 / 40.0 m = 0.225 m/s². Thus, the centripetal acceleration of the cyclist rounding a bend with a radius of 40.0 m at a speed of 3.0 m/s is 0.225 m/s².
Centripetal acceleration is a crucial factor when analyzing circular motion. In this scenario, as the cyclist negotiates a bend with a radius of 40.0 m at a speed of 3.0 m/s, the centripetal acceleration is calculated to be 0.225 m/s²
This result indicates the rate at which the cyclist is accelerating towards the center of the circular path. Understanding centripetal acceleration is fundamental for assessing the forces acting on objects in circular motion, providing insights into the dynamic aspects of the cyclist's movement around the curve.