The train travels at a speed of 72 km / h along the curve of the road. Determine the radius of the arc

The train travels at a speed of 72 km / h along the curve of the road. Determine the radius of the arc if the centripetal acceleration of the train is 1 m / s2.

Given:

v = 72 km / h – speed of the train along the curve of the road;

a = 1 m / s ^ 2 – the centripetal acceleration of the train.

It is required to determine r (meter) – the radius of the road curvature.

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

v = 72 km / h = 72 * 10/36 = 20 m / s.

Then the radius of curvature of the road will be equal to:

a = v ^ 2 / r, hence:

r = v ^ 2 / a = 20 ^ 2/1 = 400/1 = 400 meters.

Answer: the radius of curvature of the road is 400 meters.