If the minute hand of a clock is 7 cm long, find the magnitude of the average velocity of the tip of the clock’s minute hand during the time interval from 1 pm to 1.30 pm.

To solve this problem, we need to understand the concept of average velocity. Average velocity is defined as the total displacement divided by the total time taken.

Step 1: Calculate the displacement In this case, the minute hand of a clock moves from 1 pm to 1.30 pm, which is half a revolution around the clock face. This means the displacement of the tip of the minute hand is half the circumference of the circle it describes.

The formula for the circumference of a circle is 2πr, where r is the radius of the circle. Here, the length of the minute hand is the radius of the circle, which is 7 cm. So, the total circumference is 2π*7 cm = 14π cm.

Since the minute hand moves half a revolution from 1 pm to 1.30 pm, the displacement is half the circumference, which is 14π/2 cm = 7π cm.

Step 2: Calculate the time The time interval from 1 pm to 1.30 pm is 30 minutes, or 0.5 hours.

Step 3: Calculate the average velocity Now we can calculate the average velocity by dividing the total displacement by the total time. The displacement is 7π cm and the time is 0.5 hours.

So, the average velocity = displacement/time = 7π cm / 0.5 hours = 14π cm/hour.

Therefore, the magnitude of the average velocity of the tip of the clock’s minute hand during the time interval from 1 pm to 1.30 pm is 14π cm/hour.