Calculation of Velocity of Second Hand of a Clock

To calculate the velocity of the second hand of a clock at zero seconds and at fifteen seconds, we need to consider the circular motion of the hand.

Circular Motion:
Circular motion is the movement of an object along a circular path, where the object continuously changes its direction. It is characterized by the presence of a centripetal force that keeps the object moving towards the center of the circle.

Velocity:
Velocity is defined as the rate of change of displacement with respect to time. In circular motion, velocity is a vector quantity that not only considers the speed of the object but also its direction.

Given Information:
- Length of the second hand of the clock = 2 cm

Calculating Velocity at Zero Seconds:
At zero seconds, the second hand is at its starting position, pointing towards the 12 o'clock mark. Since it hasn't moved yet, its displacement is zero.

- Displacement = 0 cm
- Time = 0 seconds

Velocity is given by the formula: v = d/t, where v is the velocity, d is the displacement, and t is the time.

- Velocity at zero seconds = 0 cm/s

Calculating Velocity at Fifteen Seconds:
After fifteen seconds, the second hand has completed a quarter of a full circle, pointing towards the 3 o'clock mark. The displacement is equal to the circumference of the circle it has traveled.

- Displacement = 1/4 * circumference
- Time = 15 seconds

To calculate the circumference, we multiply the length of the second hand by 2π (pi).

- Circumference = 2 * π * 2 cm

Using the formula v = d/t, we can calculate the velocity.

- Velocity at fifteen seconds = (1/4 * circumference) / 15 cm/s

Summary:
The velocity of the second hand of a clock at zero seconds is 0 cm/s, as it has not moved from its starting position. After fifteen seconds, the velocity is calculated using the displacement and time taken. Considering the quarter circular path traveled, the velocity is given by the formula (1/4 * circumference) / 15 cm/s.