Question

Tectonic plates are large segments of the Earth's crust that move slowly. Suppose one such plate has an average speed of 7.2 cm per year.

(a) What distance does it move in 50 seconds at this speed?

 

(b) What is its speed in miles per million years?

 

Answer 1

(a) We can find the distance moved by the plate as follows:

$$d=vt,$$ $$d=\dfrac{7.2\ cm}{yr}\cdot\dfrac{1\ yr}{365\ d}\cdot\dfrac{1\ d}{24\ h}\cdot\dfrac{1\ h}{3600\ s}\cdot50\ s=1.14\cdot10^{-5}\ cm,$$ $$d=1.14\cdot10^{-5}\ cm\cdot\dfrac{1\ m}{100\ cm}\cdot\dfrac{10^9\ nm}{1\ m}=114\ nm.$$

(b)

$$v=\dfrac{7.2\ cm}{yr}\cdot\dfrac{1\cdot10^6\ yr}{1\ My}=7.2\cdot10^6\ \dfrac{cm}{My},$$ $$v=7.2\cdot10^6\ \dfrac{cm}{My}\cdot\dfrac{1\ m}{100\ cm}\cdot\dfrac{1\ mi}{1609\ m}=44.75\ \dfrac{mi}{My}.$$