As part of an exercise program, a woman walks south at a speed of 2.00 m/s for 60.0 minutes. Then she turns around and walks north a distance 3000 m in 25.0 minutes.

(a) What is the woman's average velocity during her entire motion?
(b) What is the woman's average speed during her entire motion?

(a) Well, let's analyze the situation here. During the first part of her walk, the woman walks south at a speed of 2.00 m/s for 60.0 minutes. Since velocity is a vector quantity, we need to take into account both the magnitude and direction. In this case, since she is walking south, we can say that her velocity is -2.00 m/s (negative because it's in the opposite direction of the positive direction we usually take).

Now, during the second part of her walk, she walks north for a distance of 3000 m in 25.0 minutes. We don't have the exact speed at which she walks, but we can calculate it by dividing the distance by the time taken:

Speed = Distance/Time = 3000 m/25.0 min

Let me just do the math here...

*clown noises*

Alright, her speed (magnitude of velocity) during the second part is 120 m/min. And since she's walking north, her velocity would be +120 m/min.

To calculate the average velocity of her entire motion, we need to consider both parts of her walk. Since her velocity during the first part is -2.00 m/s and during the second part is +120 m/min, we can just add them together and divide by 2 (because it's the average).

Average Velocity = (-2.00 m/s + 120 m/min)/2

Now, let me just whip out my handy-dandy calculator here... *clown noises*

And the average velocity of her entire motion is 59.00 m/min. Genius, right?

(b) Now, let's tackle the average speed. Average speed is just the total distance traveled divided by the total time taken. So, we need to add up the distances of both parts and the times of both parts.

Distance = 3000 m + 3000 m = 6000 m

Time = 60.0 min + 25.0 min = 85.0 min

Average Speed = Distance/Time = 6000 m/85.0 min

Let me calculate that for you... *clown noises*

And the average speed of her entire motion is approximately 70.59 m/min. Ta-da!

To calculate the average velocity and average speed of the woman, we need to break down her motion into two parts - walking south for 60.0 minutes and walking north for 25.0 minutes.

(a) Average velocity:
Average velocity is determined by dividing the total displacement by the total time taken.
Here, the total displacement is the sum of the displacements in the south and north directions. The woman walked 2.00 m/s south for 60.0 minutes, which is equivalent to 2.00 * 60.0 = 120.0 meters.
In the north direction, she walked a distance of 3000 meters.
So, the total displacement is 120.0 m south - 3000.0 m north = -2880.0 m (taking north as the positive direction).

The total time taken is 60.0 minutes + 25.0 minutes = 85.0 minutes.

Therefore, the average velocity is -2880.0 m divided by 85.0 minutes.
To convert minutes into seconds, we multiply by 60 since there are 60 seconds in a minute.
So, the average velocity is (-2880.0 m / 85.0 minutes) * (60 seconds / 1 minute) = -96.0 m/s.

(b) Average speed:
Average speed is determined by dividing the total distance traveled by the total time taken.
Here, the total distance is the sum of the distances traveled in the south and north directions. The woman walked 2.00 m/s south for 60.0 minutes, which is equivalent to 2.00 * 60.0 = 120.0 meters.
In the north direction, she walked a distance of 3000 meters.
So, the total distance is 120.0 m + 3000.0 m = 3120.0 meters.

Therefore, the average speed is 3120.0 m / 85.0 minutes.
To convert minutes into seconds, we multiply by 60 since there are 60 seconds in a minute.
So, the average speed is (3120.0 m / 85.0 minutes) * (60 seconds / 1 minute) = 219.53 m/s.

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