An electric model train travels at 31.50 cm/s around a circular track of radius 1.670 m. how many revolutions does it perform in one second

- - The circumference of the track is (2 · π · radius).

Circumference = (2 · π · 1.67m) = 10.49 meters.

- - The train's speed is (31.5 cm) / (10.49 m) of the track's circumference, per second. That's ...

(31.5 cm) · (1m / 100cm) / (10.49 m / circumference) =

(31.5 / 100 · 1,049) (cm · m / cm · m) =

= 0.030 of the circumference per second.

The train performs 0.03 revolution per second.

It takes (1/0.03) = about 33.3 seconds to complete one revolution of the track.