Question

A clock has a period of exactly 1 second when at rest. If you were to measure a period of 1.5 seconds for the same clock, how fast is it moving relative to you as a percentage of the speed of light?

Answer 1

To calculate the velocity of the clock relative to you, we can use the concept of time dilation in special relativity. If the clock has a period of 1.5 seconds as measured by you and its rest period is 1 second, the clock is moving at a velocity of 0.5 times the speed of light relative to you, which is 50% of the speed of light.

Step-by-step explanation:

To calculate the velocity of the clock relative to you, we can use the concept of time dilation in special relativity. According to time dilation, the perceived time interval between two events depends on the relative velocity between the observer and the events. In this case, if the clock has a period of 1.5 seconds as measured by you, and its rest period is 1 second, we can determine its velocity using the formula:

velocity = (observed period - rest period) / rest period

Plugging in the values, we get:

velocity = (1.5 seconds - 1 second) / 1 second = 0.5 seconds / 1 second = 0.5

So, the clock is moving at a velocity of 0.5 times the speed of light relative to you. To express this as a percentage of the speed of light, we multiply by 100:

velocity percentage = velocity * 100 = 0.5 * 100 = 50%