A painted dot on the circumference of the wheel is 12cm from the centre of rotation of the wheel. How far does the dot travel in 5 sec., to one decimal place?
incomplete information
(how fast is the wheel rotating ?)
To find out how far the dot travels in 5 seconds, we need to determine the distance it covers in one complete revolution.
The distance traveled in one complete revolution by any point on the circumference of a circle is equivalent to the circumference of the circle. The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius of the circle.
In this case, the painted dot is 12 cm from the center of rotation, which means the radius of the circle is 12 cm. Hence, the circumference of the wheel can be calculated as follows:
C = 2πr
C = 2π(12)
C ≈ 75.398 cm
Therefore, the dot travels approximately 75.398 cm in one complete revolution.
To determine how far the dot travels in 5 seconds, we need to calculate the fraction of a revolution covered in 5 seconds. We can use the formula D = (C × N) / T, where D is the distance traveled, C is the circumference, N is the number of revolutions, and T is the time taken.
In this case, we want to find the distance traveled in 5 seconds, so N = 1 (since it's one complete revolution) and T = 5 seconds. Plugging these values into the formula, we get:
D = (C × N) / T
D = (75.398 × 1) / 5
D ≈ 15.08 cm
Therefore, the dot travels approximately 15.08 cm in 5 seconds.