A particle moves in a circular path with a radius of 2 m and completes one revolution in 4 seconds. What is the linear speed of the particle?

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Q: A particle moves in a circular path with a radius of 2 m and completes one revolution in 4 seconds. What is the linear speed of the particle?

Solution: Circumference = 2πr = 2π(2) = 4π m. Speed = Distance/Time = 4π/4 = π m/s ≈ 3.14 m/s.

Steps: 8

Step 1: Identify the radius of the circular path, which is given as 2 meters.
Step 2: Use the formula for the circumference of a circle, which is Circumference = 2πr.
Step 3: Substitute the radius into the formula: Circumference = 2π(2) = 4π meters.
Step 4: Note that the particle completes one full revolution in 4 seconds.
Step 5: To find the linear speed, use the formula Speed = Distance / Time.
Step 6: Substitute the values into the speed formula: Speed = (4π meters) / (4 seconds).
Step 7: Simplify the equation: Speed = π meters/second.
Step 8: If needed, approximate π as 3.14 to get the speed in decimal form: Speed ≈ 3.14 m/s.