velocity-distance-time triangle Include an example problem that she how to solve for distance. time or ve

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UpStudy AI · Accepted Answer

The **Velocity-Distance-Time Triangle** is a useful visual tool that helps you understand and solve problems involving the relationships between velocity (v), distance (d), and time (t). By organizing these three variables in a triangle, you can easily see how they interrelate and determine which formula to use based on the information provided.

## The Velocity-Distance-Time Triangle

Here's how the triangle is typically structured:

```
     Distance
    ___________
    |         /
    |        /
    |       /
    |      /
 Velocity  Time
```

- **Distance (d)** is placed at the top of the triangle.
- **Velocity (v)** is on the bottom left.
- **Time (t)** is on the bottom right.

To solve for a particular variable, cover that variable in the triangle, and the formula for the remaining two variables shows up. Here's how you can interpret it:

1. **Solving for Distance (d):**
   $$
   \text{Distance} = \text{Velocity} \times \text{Time} \quad \text{(d = v × t)}
   $$

2. **Solving for Velocity (v):**
   $$
   \text{Velocity} = \frac{\text{Distance}}{\text{Time}} \quad \text{(v = d ÷ t)}
   $$

3. **Solving for Time (t):**
   $$
   \text{Time} = \frac{\text{Distance}}{\text{Velocity}} \quad \text{(t = d ÷ v)}
   $$

## Example Problem

**Problem:**  
Sarah is planning to drive to her friend's house, which is 150 kilometers away. If she travels at an average velocity of 60 kilometers per hour, how long will it take her to reach her friend?

**Given:**
- Distance (d) = 150 km
- Velocity (v) = 60 km/h
- Time (t) = ?

**Solution:**

We'll use the Velocity-Distance-Time Triangle to find the time.

1. **Identify the known variables:**
   - Distance (d) = 150 km
   - Velocity (v) = 60 km/h

2. **Determine which formula to use:**
   Since we need to find Time (t), we'll use:
   $$
   t = \frac{d}{v}
   $$

3. **Plug in the values:**
   $$
   t = \frac{150\, \text{km}}{60\, \text{km/h}} = 2.5\, \text{hours}
   $$

**Answer:**  
It will take Sarah **2.5 hours** to reach her friend's house.

## Another Example: Solving for Distance

**Problem:**  
A runner maintains a constant velocity of 8 meters per second for 45 minutes. How much distance does the runner cover?

**Given:**
- Velocity (v) = 8 m/s
- Time (t) = 45 minutes

**Solution:**

1. **Convert time to seconds (since velocity is in meters per second):**
   $$
   45\, \text{minutes} = 45 \times 60 = 2700\, \text{seconds}
   $$

2. **Use the formula to find Distance (d):**
   $$
   d = v \times t = 8\, \text{m/s} \times 2700\, \text{s} = 21600\, \text{meters}
   $$
   
3. **Convert meters to kilometers if desired:**
   $$
   21600\, \text{meters} = 21.6\, \text{kilometers}
   $$

**Answer:**  
The runner covers **21,600 meters** (or **21.6 kilometers**).

## Tips for Using the Triangle

- **Memorize the Relationships:** Understand that distance is directly proportional to both velocity and time.
- **Check Units:** Ensure that the units for velocity and time are compatible when performing calculations.
- **Rearrange Formulas When Necessary:** If you're comfortable with algebra, rearrange the formula as needed to solve for the unknown variable.

The Velocity-Distance-Time Triangle is a straightforward yet powerful tool to help you navigate problems involving these fundamental concepts in physics and everyday life scenarios.
The Velocity-Distance-Time Triangle helps solve for distance, velocity, or time by covering the variable you want to find and using the remaining two variables. For example, if you know the distance and time, you can find velocity by dividing distance by time.

velocity-distance-time triangle Include an example problem that she how to solve for distance. time or ve

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