The Length of the Minute Hand

The length of the minute hand of a clock is given as 14 cm. This means that the distance from the center of the clock to the tip of the minute hand is 14 cm.

Calculating the Speed of the Minute Hand

To calculate the speed at which the tip of the minute hand moves, we need to consider the motion of the minute hand and the time it takes to complete one full revolution.

Understanding the Motion of the Minute Hand

The minute hand of a clock moves in a circular motion around the center of the clock. This motion is uniform, which means that the minute hand covers equal distances in equal intervals of time.

Determining the Time for One Full Revolution

To calculate the speed, we need to determine the time it takes for the minute hand to complete one full revolution. In a clock, one full revolution corresponds to 60 minutes or 360 degrees.

Calculating the Speed

To calculate the speed, we use the formula:

Speed = Distance / Time

In this case, the distance covered by the tip of the minute hand in one full revolution is equal to the circumference of the circle formed by the motion of the minute hand.

The formula for the circumference of a circle is:

Circumference = 2 * π * radius

In this case, the radius is equal to the length of the minute hand, which is given as 14 cm.

Hence, the distance covered by the tip of the minute hand in one full revolution is:

Distance = 2 * π * 14 cm

Now, we know that one full revolution corresponds to 60 minutes. To convert this into hours, we divide by 60:

Time = 60 minutes / 60 minutes/hour = 1 hour

Substituting the values into the speed formula:

Speed = (2 * π * 14 cm) / 1 hour

Simplifying the expression, we have:

Speed = 2 * π * 14 cm/hour

Therefore, the speed at which the tip of the minute hand moves is 28π cm/hour.