(a) Calculate Earth’s average speed relative to the Sun.

(b) What is its average velocity over a period of one year?

Average speed is the ratio of the total distance travelled to that of the total time taken to travel that distance.

a.

Substituting values in the above equation, we get,

$\begin{array}{c}\mathrm{S}=\frac{2\times 3.14\times 1.5\times {10}^{11}\text{\hspace{0.17em}m}}{365\times 24\times 3600\text{\hspace{0.17em}s}}\\ \mathrm{S}=3\times {10}^4\text{\hspace{0.17em}m/s}\end{array}$

Hence the average speed of the earth around the sun is$\mathbf{30000}\text{\hspace{0.17em}m/s}$ .

The average velocity is the ratio of the average displacement to that of the time period.

In the case of circular motion, after one year, the earth is coming back to its initial position.

b.

Hence displacement will be zero.

$\text{Average\hspace{0.17em}velocity=}\frac{\text{Total\hspace{0.17em}Displacement}}{\text{Total\hspace{0.17em}Time}}$

Substituting values in the above equation, we get,

$\begin{array}{c}\mathrm{V}=\frac{0}{1\mathrm{year}}\\ \mathrm{V}=\frac{0}{365\times 24\times 3600}\\ \mathrm{V}=0\text{\hspace{0.17em}m/s}\end{array}$

Hence the velocity will be zero, and the speed will be 0 m/s.