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Q5PE

Expert-verifiedFound in: Page 82

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

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

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

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.

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

**a. **

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

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

**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,

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

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

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