College Physics Problem 1.9

Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year.
(a) What distance does it move in 1.0 s at this speed?
(b) What is its speed in kilometers per million years?


Part a

We know that the formula for the distance traveled, d, if we are given rate, r, and time, t is given by \displaystyle d=r\times t

Therefore, the distance traveled is 

\displaystyle d=\left(4\:\frac{cm}{year}\times \frac{1\:year}{365\:\frac{1}{4}\:days}\times \frac{1\:day}{24\:hours}\times \frac{1\:hour}{60\:mins}\times \frac{1\:min}{60\:s}\right)\left(1\:s\right)

\displaystyle d=1.3\times 10^{-7}\:cm\:

\displaystyle d=1.3\times 10^{-9}\:m

Therefore, the distance traveled by the tectonic plate is about \displaystyle 1.3\times 10^{-9}\:m          ☚

Part b

We need to convert 4.0 cm/year to km/My. 

\displaystyle 4.0\:\frac{cm}{year}\times \frac{1\:m}{100\:cm}\times \frac{1\:km}{1000\:m}\times \frac{1\:000\:000\:years}{1\:My}=40\:\frac{km}{My}

Therefore, the speed of the tectonic plates is 40 km/My.          ☚