5. (a) calculate earth’s average speed relative to the sun. (b) what is its average velocity over a period…

Explanation:

Step1: Recall formula for average speed

Average speed $v_{avg - speed}=\frac{d}{t}$, where $d$ is the total distance traveled and $t$ is the time - interval. The Earth travels in an approximately circular orbit around the Sun with a radius $r\approx1.5\times 10^{11}\ m$. The distance it travels in one year (its orbital circumference) is $d = 2\pi r$. The time - interval $t = 1\ year=365\times24\times3600\ s$.

Step2: Calculate the distance

$d = 2\pi r=2\pi\times(1.5\times 10^{11}\ m)\approx9.42\times 10^{11}\ m$.

Step3: Calculate the time

$t=365\times24\times3600\ s\approx3.156\times 10^{7}\ s$.

Step4: Calculate average speed

$v_{avg - speed}=\frac{d}{t}=\frac{9.42\times 10^{11}\ m}{3.156\times 10^{7}\ s}\approx29.8\times10^{3}\ m/s = 29.8\ km/s$.

Step5: Recall formula for average velocity

Average velocity $\vec{v}_{avg}=\frac{\Delta\vec{x}}{t}$, where $\Delta\vec{x}$ is the displacement. In one - year, the Earth returns to its original position relative to the Sun, so the displacement $\Delta\vec{x}=0$.

Step6: Calculate average velocity

$\vec{v}_{avg}=\frac{\Delta\vec{x}}{t}=\frac{0}{3.156\times 10^{7}\ s}=0\ m/s$.

Answer:

(a) $29.8\ km/s$ (b) $0\ m/s$