Jeff Hiked For 2 Hours And Traveled 5 Miles. If He Continues At The Same Pace, Which Equation Will Show The Relationship Between The Time, $t$, In Hours He Hikes To Distance, $d$, In Miles? Will The Graph Be Continuous Or Discrete?A.

Introduction

In this article, we will explore the relationship between time and distance when hiking at a constant pace. We will use the given information about Jeff's hike to determine the equation that represents this relationship. Additionally, we will discuss the nature of the graph that represents this relationship.

Given Information

Jeff hiked for 2 hours and traveled 5 miles. If he continues at the same pace, we need to find the equation that shows the relationship between the time, $t$, in hours he hikes to distance, $d$, in miles.

Equation of Motion

The equation of motion that represents the relationship between time and distance is given by:

$$d = vt$$

where $d$ is the distance traveled, $v$ is the velocity (or speed), and $t$ is the time.

Finding the Velocity

We are given that Jeff hiked for 2 hours and traveled 5 miles. We can use this information to find the velocity:

$$v = \frac{d}{t} = \frac{5}{2} = 2.5 \text{ miles/hour}$$

Equation of Motion with Velocity

Now that we have found the velocity, we can substitute it into the equation of motion:

$$d = 2.5t$$

This is the equation that shows the relationship between the time, $t$, in hours Jeff hikes to distance, $d$, in miles.

Graph of the Equation

The graph of the equation $d = 2.5t$ is a straight line with a positive slope. This is because the equation represents a linear relationship between the time and distance.

Continuous or Discrete Graph

The graph of the equation $d = 2.5t$ is a continuous graph. This is because the equation represents a smooth, continuous relationship between the time and distance.

Conclusion

In this article, we have explored the relationship between time and distance when hiking at a constant pace. We have used the given information about Jeff's hike to determine the equation that represents this relationship. We have also discussed the nature of the graph that represents this relationship. The equation is $d = 2.5t$, and the graph is a continuous straight line.

Real-World Applications

The equation $d = 2.5t$ has many real-world applications. For example, it can be used to plan a hike or a road trip. It can also be used to calculate the time it takes to travel a certain distance at a constant speed.

Example Problems

1. If Jeff hikes for 4 hours, how far will he travel?
2. If Jeff hikes for 1 hour, how far will he travel?
3. If Jeff hikes at a constant pace of 2.5 miles/hour, how far will he travel in 6 hours?

Answer Key

1. $d = 2.5(4) = 10$ miles
2. $d = 2.5(1) = 2.5$ miles
3. $d = 2.5(6) = 15$ miles

Final Thoughts

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Introduction

In our previous article, we explored the relationship between time and distance when hiking at a constant pace. We determined the equation that represents this relationship and discussed the nature of the graph that represents this relationship. In this article, we will answer some frequently asked questions about the relationship between time and distance.

Q: What is the equation that represents the relationship between time and distance?

A: The equation that represents the relationship between time and distance is:

$$d = vt$$

where $d$ is the distance traveled, $v$ is the velocity (or speed), and $t$ is the time.

Q: How do I find the velocity?

A: To find the velocity, you need to know the distance traveled and the time taken. You can use the formula:

$$v = \frac{d}{t}$$

Q: What if I don't know the velocity?

A: If you don't know the velocity, you can use the equation:

$$d = vt$$

to find the distance traveled. You will need to know the time taken and the velocity.

Q: Is the graph of the equation continuous or discrete?

A: The graph of the equation $d = vt$ is a continuous graph. This is because the equation represents a smooth, continuous relationship between the time and distance.

Q: What are some real-world applications of the equation?

A: The equation $d = vt$ has many real-world applications. For example, it can be used to plan a hike or a road trip. It can also be used to calculate the time it takes to travel a certain distance at a constant speed.

Q: Can I use the equation to plan a hike?

A: Yes, you can use the equation to plan a hike. For example, if you know the distance you want to hike and the time you have available, you can use the equation to determine the velocity you need to maintain.

Q: Can I use the equation to calculate the time it takes to travel a certain distance?

A: Yes, you can use the equation to calculate the time it takes to travel a certain distance. For example, if you know the distance you want to travel and the velocity you will maintain, you can use the equation to determine the time it will take.

Q: What if I'm not hiking at a constant pace?

A: If you're not hiking at a constant pace, you will need to use a different equation to represent the relationship between time and distance. This equation will depend on the specific circumstances of your hike.

Q: Can I use the equation to plan a road trip?

A: Yes, you can use the equation to plan a road trip. For example, if you know the distance you want to travel and the time you have available, you can use the equation to determine the velocity you need to maintain.

Q: What are some other equations that represent the relationship between time and distance?

A: There are many other equations that represent the relationship between time and distance. Some examples include:

• $d = \frac{1}{2}at^2$ (equation of motion under constant acceleration)
• $d = \frac{1}{2}gt^2$ (equation of motion under constant gravity)
• $d = vt + \frac{1}{2}at^2$ (equation of motion under constant acceleration and gravity)

Conclusion

In this article, we have answered some frequently asked questions about the relationship between time and distance. We have discussed the equation that represents this relationship and some of its real-world applications. We have also discussed some other equations that represent the relationship between time and distance.