A cyclist is moving in a circular track of radius 30 m. If he completes one roun

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Question: A cyclist is moving in a circular track of radius 30 m. If he completes one round in 12 seconds, what is his average speed?

Options:

Correct Answer: 10 m/s

Solution:

Circumference = 2πr = 2π(30) = 60π m. Average speed = distance/time = 60π m / 12 s = 5 m/s.

A cyclist is moving in a circular track of radius 30 m. If he completes one round in 12 seconds, what is his average speed?

A cyclist is moving in a circular track of radius 30 m. If he completes one round in 12 seconds, what is his average speed?

Correct Answer: 5 m/s

Step 1: Identify the radius of the circular track, which is given as 30 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(30).
Step 4: Calculate the circumference: Circumference = 60π meters.
Step 5: Note that the cyclist completes one round of the track, which means he travels the circumference distance.
Step 6: The time taken to complete one round is given as 12 seconds.
Step 7: Use the formula for average speed, which is Average Speed = Distance / Time.
Step 8: Substitute the values into the formula: Average Speed = 60π meters / 12 seconds.
Step 9: Simplify the calculation: Average Speed = 5π meters per second.
Step 10: If needed, approximate π as 3.14 to find a numerical value for average speed.

Circular Motion – Understanding the relationship between distance traveled in a circular path and the time taken to complete that distance.
Average Speed Calculation – Calculating average speed using the formula: average speed = total distance / total time.
Circumference of a Circle – Using the formula for the circumference of a circle (C = 2πr) to determine the distance traveled in one complete round.