A cyclist moving on a corcular track of radius 40m completes half a revolution in 40 sec. Its average velocity is nearly
angular velocity: 2π/40 = π/20 rad/s
speed: 40πm/40s = π m/s
velocity: -80m/40s = -2 m/s in the direction from start to finish.
To find the average velocity of the cyclist, we need to first calculate the distance covered.
The distance covered by the cyclist in half a revolution of a circular track can be calculated using the formula:
Distance = Circumference of the track * Number of revolutions
Since the cyclist completes half a revolution, the number of revolutions is 1/2, and the circumference of the circular track can be calculated using the formula:
Circumference = 2 * π * radius
Given that the radius of the circular track is 40m, we can substitute the values into the formulas:
Circumference = 2 * π * 40m = 80π m
Now, we can calculate the distance covered by the cyclist:
Distance = 80π m * 1/2 = 40π m
Next, we can calculate the average velocity using the formula:
Average Velocity = Distance / Time
Given that the time taken to complete half a revolution is 40 seconds, we can substitute the values into the formula:
Average Velocity = 40π m / 40 sec = π m/sec
Therefore, the average velocity of the cyclist is approximately π m/sec, which is roughly 3.14 m/sec (taking π ≈ 3.14).
So, the average velocity of the cyclist is nearly 3.14 m/sec.