a woman walks along a circular path of radius of 15m it takes her 2min to get halfway around the path at this halfway point what is her approximate distance traveled, displacement, average speed in m/s, and average velocity in m/s?
d = pi*2r/2 = 3.14*30/2 = 47.1 m.
D = 2*r = 2*15 = 30 m.
r*t = 47.1, r = 47.1/t = 47.1m/120s. = 0.39 m/s.
V = D/t = 30m/120s = 0.25 m/s.
To find the approximate distance traveled, displacement, average speed, and average velocity, we can follow these steps:
Step 1: Calculate the circumference of the circular path.
The formula for the circumference (C) of a circle is given by C = 2πr, where r is the radius.
Given:
Radius (r) = 15 meters
Using the formula, we can calculate the circumference:
C = 2π(15) ≈ 94.25 meters
Step 2: Calculate the distance traveled.
Since the woman walks halfway around the circular path, the distance traveled will be half of the circumference.
Distance = 1/2 * Circumference
Distance = 1/2 * 94.25 ≈ 47.125 meters
Therefore, the approximate distance traveled by the woman is approximately 47.125 meters.
Step 3: Calculate the displacement.
Displacement is calculated as the shortest distance between the starting point and the ending point. In this case, since the woman walks halfway around the circular path, her displacement is equal to the radius.
Displacement = Radius
Displacement = 15 meters
Therefore, the approximate displacement of the woman is 15 meters.
Step 4: Calculate the average speed.
Average speed is calculated by dividing the total distance traveled by the total time taken. In this case, the total time taken is given as 2 minutes.
Average Speed = Distance / Time
Average Speed = 47.125 meters / 2 minutes
To convert minutes to seconds, we multiply by 60:
Average Speed = 47.125 meters / (2 minutes * 60 seconds/minute)
Average Speed ≈ 0.3927 meters/second
Therefore, the average speed of the woman is approximately 0.3927 meters/second.
Step 5: Calculate the average velocity.
Average velocity is calculated by dividing the total displacement by the total time taken. In this case, the total time taken is given as 2 minutes.
Average Velocity = Displacement / Time
Average Velocity = 15 meters / 2 minutes
To convert minutes to seconds, we multiply by 60:
Average Velocity = 15 meters / (2 minutes * 60 seconds/minute)
Average Velocity ≈ 0.125 meters/second
Therefore, the average velocity of the woman is approximately 0.125 meters/second.
To summarize:
- The approximate distance traveled by the woman is 47.125 meters.
- The approximate displacement of the woman is 15 meters.
- The average speed of the woman is approximately 0.3927 meters/second.
- The average velocity of the woman is approximately 0.125 meters/second.
To find the approximate distance traveled, displacement, average speed, and average velocity, we need to understand a few concepts and formulas:
1. Circumference of a Circle: The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.
2. Distance Traveled: This is the total length covered along the circular path. To find this, we can calculate the circumference of the circle using the given radius.
3. Displacement: This is the change in position or the distance between the initial and final points. For a circular path, the displacement is the diameter of the circle.
4. Average Speed: Average speed is given by the formula Avg. Speed = Total Distance / Total Time. We can calculate this using the distance traveled and the time taken.
5. Average Velocity: Average velocity is the displacement divided by the total time taken. We can calculate this using the displacement and the time taken.
Now let's calculate each of these values step by step:
1. Distance Traveled:
- Given radius of the circle, r = 15m.
- Using the formula for the circumference of a circle, C = 2πr.
- Plugging in the value, C = 2π(15) ≈ 94.25m.
- The approximate distance traveled is 94.25m.
2. Displacement:
- The halfway point of the circular path is the opposite side of the initial point.
- The diameter of the circle represents the displacement.
- Thus, the displacement is 2r = 2(15) = 30m.
3. Average Speed:
- From the given information, we know that she takes 2 minutes to travel halfway around the path.
- Average Speed = Total Distance / Total Time.
- Plugging in the values, Average Speed = 94.25m / 2min.
- Converting minutes to seconds (1 min = 60s), Average Speed ≈ 94.25m / 120s ≈ 0.785 m/s.
4. Average Velocity:
- Average Velocity = Displacement / Total Time.
- Plugging in the values, Average Velocity = 30m / 120s = 0.25 m/s.
Therefore, based on the given information, the approximate distance traveled is 94.25m, the displacement is 30m, the average speed is 0.785 m/s, and the average velocity is 0.25 m/s.