# A motorcyclist, moving in a circus arena, drives a circle with a radius of 13m in 8 seconds.

A motorcyclist, moving in a circus arena, drives a circle with a radius of 13m in 8 seconds. Determine the path and module of movement of the motorcyclist: a) in 4 seconds of movement; b) in 8 seconds of movement?

Given: R (radius of the circus arena) = 13 m; t (time per lap) = 8 s (T (period) = 8 s).

1) Angular velocity: ω = 2 * Π / T = Π / 4.

2) Linear speed: V = ω * R = Π * R / 4.

3) Path in 4 s: S1 = V * t1 = Π * R / 4 * 4 = 3.14 * 13 = 40.82 m.

Displacement modulus: φ1 (angle of rotation) = ω * t1 = Π / 4 * 4 = Π = 180º, therefore, S1.1 = 2R = 2 * 13 = 26 m.

4) Path in 8 s: S1 = V * t2 = 3.14 * 13/4 * 8 = 81.64 m.

Displacement modulus: φ2 = ω * t2 = Π / 4 * 8 = 2Π = 360º, therefore S2.2 = 0 m.

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