What is the radius of curvature of the bridge if a centripetal acceleration of 2.5 m / s acts

What is the radius of curvature of the bridge if a centripetal acceleration of 2.5 m / s acts on a bus traveling along it at a speed of 54 km / h?

Given:

v = 54 km / h (kilometers per hour) – the speed of a car moving across the bridge;

a = 2.5 m / s2 (meters per second squared) is the centripetal acceleration acting on the vehicle.

It is required to determine R (meter) – the radius of curvature of the bridge.

Let’s convert the units of measurement of speed to the SI system:

v = 54 km / h = 54 * 10/36 = 540/36 = 15 m / s (meters per second).

Then, to determine the radius, you must use the following formula:

a = v ^ 2 / R, from here we find that:

R = v ^ 2 / a = 15 ^ 2 / 2.5 = 225 / 2.5 = 2250/25 = 90 meters.

Answer: the radius of curvature of the bridge is 90 meters.