To calculate the tangential velocity of a car moving in a circle, you need to know the radius of the circle and the time it takes to complete a revolution.
Given: Radius (r) = 10 m Number of revolutions (n) = 7 Time (t) = 0.25 s
First, let's calculate the total distance covered by the car. The distance covered in one revolution is equal to the circumference of the circle:
Circumference = 2πr
Distance covered = Circumference × Number of revolutions
Distance covered = 2πr × n
Next, we can calculate the tangential velocity. Tangential velocity is defined as the distance traveled per unit time.
Tangential velocity = Distance covered ÷ Time
Tangential velocity = (2πr × n) ÷ t
Substituting the given values:
Tangential velocity = (2π × 10 × 7) ÷ 0.25
Tangential velocity = (140π) ÷ 0.25
Tangential velocity ≈ 1754.955 m/s (rounded to three decimal places)
Therefore, the tangential velocity of the car moving in a circle with a radius of 10 m and completing 7 revolutions in 0.25 seconds is approximately 1754.955 m/s.