Question

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 s at this speed? (b) what is its speed in kilometers per million years?

Explanation:

Step1: Convert years to seconds

1 year = 365 days, 1 day = 24 hours, 1 hour = 60 minutes, 1 minute = 60 seconds. So 1 year = 365×24×60×60 s = 31536000 s.

Step2: Find distance in 1 s

The speed $v = 4.0$ cm/year. To find the distance $d$ in 1 s, we use the formula $d=\frac{v}{31536000}$. Substituting $v = 4.0$ cm/year, we get $d=\frac{4.0}{31536000}$ cm/s $\approx1.27\times10^{-7}$ cm/s. Since 1 cm = 0.01 m, $d = 1.27\times10^{-9}$ m.

Step3: Convert speed to km/million - years

1 km = 100000 cm. 1 million years = 1000000 years.
The speed $v = 4.0$ cm/year. In km/million - years, we first convert cm to km and years to million - years. $v=\frac{4.0\times10^{-5}\text{ km}}{1\text{ year}}\times1000000\text{ years/million - year}=40$ km/million - year.

Answer:

(a) $1.27\times10^{-9}$ m
(b) 40 km/million - year