To find the average velocity and average speed of a particle moving along a circular path, we need to calculate the total displacement and total distance traveled by the particle.
The total displacement of the particle is zero because it completes a full revolution, returning to its starting point. Therefore, the average velocity is also zero.
The total distance traveled by the particle is equal to the circumference of the circular path. The formula for the circumference of a circle is given by:
C = 2πr
where C is the circumference and r is the radius of the circle.
In this case, the radius is 2 meters, so the circumference is:
C = 2π(2) = 4π meters
Now we can calculate the average speed using the formula:
Average speed = Total distance / Total time
Given that the particle completes a revolution within 10 seconds, the total time is 10 seconds.
Average speed = 4π meters / 10 seconds
Calculating this value, we get:
Average speed ≈ 1.26 meters per second (rounded to two decimal places)
To summarize:
- The average velocity is 0 meters per second.
- The average speed is approximately 1.26 meters per second.