Part 2: Time Interval ProblemsUse The Formula: \[$\Delta T = T_f - T_i\$\]4. A Race Starts At \[$2 \, \text{s}\$\] And Finishes At \[$22 \, \text{s}\$\]. What Is The Time Interval?5. A Runner Begins A Workout At 10:30 AM And

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Introduction

In the previous part of this series, we discussed the concept of time intervals and how to calculate them using the formula {\Delta t = t_f - t_i$}$. In this part, we will continue to explore time interval problems and provide step-by-step solutions to help you understand the concept better.

What is a Time Interval?

A time interval is the difference between two points in time. It is a measure of the duration between two events or points in time. Time intervals can be measured in seconds, minutes, hours, days, weeks, months, or years, depending on the context.

Calculating Time Intervals

To calculate a time interval, we use the formula {\Delta t = t_f - t_i$}$, where {\Delta t$}$ is the time interval, {t_f$}$ is the final time, and {t_i$}$ is the initial time.

Example 1: A Race Starts at 2 s and Finishes at 22 s

A race starts at ${2 \, \text{s}\$} and finishes at ${22 \, \text{s}\$}. What is the time interval?

To solve this problem, we will use the formula {\Delta t = t_f - t_i$}$.

  • {t_i = 2 , \text{s}$}$
  • {t_f = 22 , \text{s}$}$

Substituting these values into the formula, we get:

{\Delta t = 22 , \text{s} - 2 , \text{s} = 20 , \text{s}$}$

Therefore, the time interval is ${20 \, \text{s}\$}.

Example 2: A Runner Begins a Workout at 10:30 AM

A runner begins a workout at 10:30 AM and finishes at 11:45 AM. What is the time interval?

To solve this problem, we will use the formula {\Delta t = t_f - t_i$}$.

  • {t_i = 10:30 , \text{AM}$}$
  • {t_f = 11:45 , \text{AM}$}$

First, we need to convert the times to a common unit. We will convert both times to minutes.

  • {t_i = 10:30 , \text{AM} = 630 , \text{min}$}$
  • {t_f = 11:45 , \text{AM} = 705 , \text{min}$}$

Substituting these values into the formula, we get:

{\Delta t = 705 , \text{min} - 630 , \text{min} = 75 , \text{min}$}$

Therefore, the time interval is ${75 \, \text{min}\$}.

Example 3: A Car Travels from City A to City B

A car travels from City A to City B in 3 hours and 45 minutes. What is the time interval?

To solve this problem, we will use the formula {\Delta t = t_f - t_i$}$.

  • {t_i = 0 , \text{h}$}$
  • {t_f = 3 , \text{h} + 45 , \text{min} = 3.75 , \text{h}$}$

Substituting these values into the formula, we get:

{\Delta t = 3.75 , \text{h} - 0 , \text{h} = 3.75 , \text{h}$}$

Therefore, the time interval is ${3.75 \, \text{h}\$}.

Conclusion

In this part, we discussed time interval problems and provided step-by-step solutions to help you understand the concept better. We used the formula {\Delta t = t_f - t_i$}$ to calculate time intervals in various scenarios. We also converted times to a common unit to facilitate the calculation.

Practice Problems

  1. A runner begins a workout at 9:00 AM and finishes at 10:15 AM. What is the time interval?
  2. A car travels from City A to City B in 2 hours and 30 minutes. What is the time interval?
  3. A race starts at 5:00 PM and finishes at 6:15 PM. What is the time interval?

Answer Key

  1. ${75 \, \text{min}\$}
  2. ${2.5 \, \text{h}\$}
  3. ${1.25 \, \text{h}\$}

References

Introduction

In the previous parts of this series, we discussed the concept of time intervals and how to calculate them using the formula {\Delta t = t_f - t_i$}$. In this part, we will answer some frequently asked questions about time intervals to help you better understand the concept.

Q&A

Q1: What is the difference between a time interval and a duration?

A1: A time interval is the difference between two points in time, while a duration is the length of time between two events or points in time. In other words, a time interval is a measure of the time between two events, while a duration is a measure of the length of time an event lasts.

Q2: How do I calculate a time interval if the times are not in the same unit?

A2: To calculate a time interval if the times are not in the same unit, you need to convert both times to a common unit. For example, if you have a time interval in hours and minutes, you can convert both times to minutes and then subtract the initial time from the final time.

Q3: Can I use a negative time interval?

A3: No, you cannot use a negative time interval. Time intervals are always positive, as they represent the difference between two points in time. If you get a negative time interval, it means that the final time is before the initial time, which is not possible.

Q4: How do I calculate a time interval if the times are in different formats?

A4: To calculate a time interval if the times are in different formats, you need to convert both times to a common format. For example, if you have a time interval in 12-hour format and the other time in 24-hour format, you can convert both times to 24-hour format and then subtract the initial time from the final time.

Q5: Can I use a time interval to calculate the speed of an object?

A5: Yes, you can use a time interval to calculate the speed of an object. If you know the distance traveled and the time interval, you can use the formula {\text{speed} = \frac{\text{distance}}{\text{time interval}}$}$ to calculate the speed of the object.

Q6: How do I calculate a time interval if the times are in different time zones?

A6: To calculate a time interval if the times are in different time zones, you need to convert both times to a common time zone. For example, if you have a time interval in Pacific Standard Time (PST) and the other time in Eastern Standard Time (EST), you can convert both times to PST and then subtract the initial time from the final time.

Q7: Can I use a time interval to calculate the time of day?

A7: Yes, you can use a time interval to calculate the time of day. If you know the initial time and the time interval, you can use the formula {\text{final time} = \text{initial time} + \text{time interval}$}$ to calculate the final time.

Q8: How do I calculate a time interval if the times are in different calendars?

A8: To calculate a time interval if the times are in different calendars, you need to convert both times to a common calendar. For example, if you have a time interval in the Gregorian calendar and the other time in the Julian calendar, you can convert both times to the Gregorian calendar and then subtract the initial time from the final time.

Conclusion

In this part, we answered some frequently asked questions about time intervals to help you better understand the concept. We discussed how to calculate time intervals in various scenarios, including when the times are not in the same unit, when the times are in different formats, and when the times are in different time zones.

Practice Problems

  1. A runner begins a workout at 9:00 AM and finishes at 10:15 AM. What is the time interval?
  2. A car travels from City A to City B in 2 hours and 30 minutes. What is the time interval?
  3. A race starts at 5:00 PM and finishes at 6:15 PM. What is the time interval?

Answer Key

  1. ${75 \, \text{min}\$}
  2. ${2.5 \, \text{h}\$}
  3. ${1.25 \, \text{h}\$}

References