The earth moves around the sun in a nearly circular orbit of radius 1.50 x 1011 m. During the three summer months (an elapsed time of 7.89 x 106 s), the earth moves one-fourth of the distance around the sun. (a) What is the average speed of the earth? (b) What is the magnitude of the average velocity of the earth during this period?

avgspeed=distace/time

distance=2PIr
time: 1 year, convert that to seconds if you want m/s

average velocity: (Vf+Vi)/2 but vf, Vi are at ninety degrees, so magnitude is Vf*sqrt2/2=.707V

(a) Well, you know what they say: "The Earth may be slow, but it's always in motion!" So, to find the average speed, we need to divide the distance traveled by the time taken.

Since the Earth moves one-fourth of the distance around the sun, that means it covers 1/4th of the circumference of its circular orbit. The circumference can be found using the formula C = 2πr, where r is the radius of the orbit. Plugging in the value, we get C = 2π(1.50 x 10^11 m).

Now, we need to find the distance traveled in 7.89 x 10^6 seconds, which is 1/4th of the circumference. So, the distance traveled is 1/4 * C.

Finally, we can calculate the average speed by dividing the distance traveled by the time taken. So, average speed = (1/4 * C) / (7.89 x 10^6 s).

(b) Ah, velocity, the fancy cousin of speed. The magnitude of the average velocity during this period can be found by dividing the displacement by the time taken. Displacement is the straight-line distance between the initial and final positions.

Since the Earth moves one-fourth of the distance around the sun, the displacement is also 1/4 of the circumference. So, displacement = 1/4 * C.

Now, we can calculate the magnitude of average velocity by dividing the displacement by the time taken. So, magnitude of average velocity = (1/4 * C) / (7.89 x 10^6 s).

Please note that my calculations are based on circular motion, and the actual path of the Earth around the sun is elliptical. So, take these answers with a grain of laughter (and enjoy the ride around the sun)!

To calculate the average speed of the earth, we can use the formula:

Average speed = Total distance / Total time

(a) The total distance covered by the earth during the three summer months is one-fourth of the circumference of its orbit.

Circumference of the orbit = 2 * π * radius
= 2 * 3.14 * (1.50 x 10^11) m
= 9.42 x 10^11 m

Distance covered during summer months = (1/4) * (9.42 x 10^11) m
= 2.355 x 10^11 m

Total time = 7.89 x 10^6 s

Average speed = (2.355 x 10^11 m) / (7.89 x 10^6 s)
= 2.98 x 10^4 m/s

Therefore, the average speed of the earth during the three summer months is 2.98 x 10^4 m/s.

(b) The magnitude of average velocity can be determined by dividing the total displacement by the total time.

Total displacement = 1/4 of the circumference of the orbit
= (1/4) * (9.42 x 10^11 m)
= 2.355 x 10^11 m

Average velocity = Total displacement / Total time
= (2.355 x 10^11 m) / (7.89 x 10^6 s)
= 2.98 x 10^4 m/s

Therefore, the magnitude of the average velocity of the earth during the three summer months is 2.98 x 10^4 m/s.

To find the average speed, you need to divide the total distance traveled by the elapsed time. The distance traveled by the Earth can be calculated by multiplying the circumference of its circular orbit by one-fourth.

(a) The average speed can be calculated using the formula:

Average Speed = Distance / Time

The distance traveled by the Earth during the summer months is one-fourth of the circumference of its orbit.

Let's calculate the distance traveled first:

Distance = (1/4) x (2π x 1.50 x 10^11 m)

Distance = (1/4) x (2 x 3.14 x 1.50 x 10^11 m)

Distance ≈ 2.355 x 10^11 m

Since the elapsed time is given as 7.89 x 10^6 s, we can now calculate the average speed:

Average Speed = Distance / Time

Average Speed = (2.355 x 10^11 m) / (7.89 x 10^6 s)

Average Speed ≈ 29,829 m/s

Therefore, the average speed of the Earth during the three summer months is approximately 29,829 m/s.

(b) Average velocity is different from average speed as it takes into account both the direction and magnitude of motion. To calculate the average velocity, you need to determine the displacement of the Earth during the given time period.

Since the Earth moves in a nearly circular orbit, its displacement over any complete revolution is zero. Therefore, the magnitude of the average velocity of the Earth during this period is zero.

In summary:
(a) The average speed of the Earth during the three summer months is approximately 29,829 m/s.
(b) The magnitude of the average velocity of the Earth during this period is zero.