Q5PE - College Physics (Urone)

Question

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

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

Step-by-Step Solution

Answer

a.  Earth’s average speed related to Sun is  $3\times {10}^4\text{\hspace{0.17em}m/s}$.

b. The average velocity of the earth is zero.

Step 1: Average speed of earth around the Sun

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

a. 

$\begin{array}{c}\text{Average\hspace{0.17em}Speed}=\frac{\text{Total\hspace{0.17em}Distance}}{\text{Total\hspace{0.17em}Time}}\\ \mathrm{S}=\frac{\text{Circumference\hspace{0.17em}of\hspace{0.17em}earth's\hspace{0.17em}orbit\hspace{0.17em}around\hspace{0.17em}sun}}{\text{1\hspace{0.17em}year}}\\ \mathrm{S}=\frac{2\mathrm{\pi R}}{1\mathrm{year}}\end{array}$

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 $\mathbf{30000}\text{\hspace{0.17em}m/s}$ . 

Step 2: Average Velocity of the earth around the Sun

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.