The chain of the Hawaiian Islands can be used to calculate the rate of movement of the Pacific Plate over the last few million y
ears. The island of Hawaii currently sits on the hot spot, and is therefore 0 million years old. The island of Kauai used to sit on the hot spot; it is approximately 5.1 million years old and is now approximately 473 km away from the hot spot, to the northwest. Given these parameters, what is the average rate of motion of the Pacific Plate in centimeters per year?
Let d(t₀) represent the initial position of Kauai island = 0 km from the hot spot. at time t = 0 million years. Let d(t₁) represent its final position at time t₁ = 5.1 million years later in the North - west direction. d(t₁)=473 km = 4.73 × 10³ cm. The average speed v = total distance/ total time =[d(t₁) - d(t₀)]/t₁₋t₀ = (4.73 × 10³ - 0)/(5.1 × 10⁶ - 0) = 4.73/5.1 × 10³⁻⁶ = 9.275 × 10⁻⁴ cm/year ≅ 9.28 × 10⁻⁴ cm/year
