Calculate the earth's average speed relative to the sun. b. what is the earth's average velocity over a period of one year?

The correct values are;

a. The average speed of the Earth relative to the Sun is approximately 29,785.68 m/s

b. The average velocity of the Earth over a period of one year is 0

The reason the above values are correct are given as follows;

The total distance traveled by the Earth relative to the Sun, is given by the length of the orbit of the Earth around the Sun ≈ 2 × × π

Where;

 = The average distance at which the Earth orbits around the Sun = 149.60 million km

Distance traveled by Earth ≈ 2 × 149.6 × 10⁹ × π

The time it takes to revolve once around the Sun = 365.25 days

365.25 days =

The average speed of the Earth relative to the Sun ≈ 29,785.68 m/s

b.

The Earth's average velocity over a period of one year is given as follows;

Total displacement of the Earth = Final position - Initial position

The motion of the Earth round the Sun is circular, and in a period of one year, the Earth revolves once round the Sun

Therefore, after exactly one year, relative to the Sun;

Final position of the Earth = Initial position of the Earth

Relative to the Sun, in one year, we have;

Displacement = Final position of the Earth - Initial position of the Earth = 0

Therefore;

The Earth is located in the same place relative to the Sun after a period of one year

Learn more about average speed and average velocity here:

link

a).  The Earth travels around the sun in a path that's nearly a circle, with a radius of roughly 93 million miles.

The circumference of the circle is (2 · π · radius) = about  5.843 x 10⁸  miles.

Average Speed = (distance covered) / (time to cover the distance)

The time to cover the distance is 1 year.

Speed = (5.843 x 10⁸ mile/year) (year / 365 day) (day / 24 hour)

Speed = (5.843 x 10⁸ / 365·24) (mile · year · day / year · day · hour)

Average speed = 66,705 miles/hour .

b). The Earth's average velocity over a period of 1 year is zero.

Velocity = (displacement) / (time)

Displacement = (distance and direction between start-point and end-point). After one year, the Earth is located at the point where it started, so its displacement over the period of 1 year is zero.