Determining the distance traveled when given the velocity and time is a fundamental concept in physics and everyday life. This article will guide you through the process using a simple algebraic formula.
Formula to Find Distance
The relationship between velocity (\( v \)), distance (\( d \)), and time (\( t \)) is expressed with the formula:
\[ v = \dfrac{d}{t} \]
To find the distance (\( d \)), we rearrange the formula:
\[ d = v \cdot t \]
where:
- \( v \) is the velocity (or speed) in meters per second (\(\text{m/s}\)).
- \( t \) is the time in seconds (\(\text{s}\)).
- \( d \) is the distance in meters (\(\text{m}\)).
Example 1: Calculating Distance for a Moving Car
Given:
- Velocity (\( v \)) = \( 20 \, \text{m/s} \)
- Time (\( t \)) = \( 15 \, \text{s} \)
Step-by-Step Calculation:
Step 1: Substitute the Values into the Distance Formula
\[ d = v \cdot t \]
\[ d = 20 \cdot 15 \]
Step 2: Perform the Multiplication
\[ d = 300 \]
Final Value
The distance traveled by the car is:
\[ d = 300 \, \text{m} \]
Example 2: Finding Distance Covered by a Runner
Given:
- Velocity (\( v \)) = \( 8 \, \text{m/s} \)
- Time (\( t \)) = \( 30 \, \text{s} \)
Step-by-Step Calculation:
Step 1: Substitute the Values into the Distance Formula
\[ d = v \cdot t \]
\[ d = 8 \cdot 30 \]
Step 2: Perform the Multiplication
\[ d = 240 \]
Final Value
The distance covered by the runner is:
\[ d = 240 \, \text{m} \]
Example 3: Calculating Distance Traveled by a Cyclist
Given:
- Velocity (\( v \)) = \( 12 \, \text{m/s} \)
- Time (\( t \)) = \( 25 \, \text{s} \)
Step-by-Step Calculation:
Step 1: Substitute the Values into the Distance Formula
\[ d = v \cdot t \]
\[ d = 12 \cdot 25 \]
Step 2: Perform the Multiplication
\[ d = 300 \]
Final Value
The distance traveled by the cyclist is:
\[ d = 300 \, \text{m} \]
