Understanding how to calculate velocity when you know the distance traveled and the time taken is essential in physics and various real-life applications. This article will walk you through the process using a simple algebraic formula.
Formula to Find Velocity
The relationship between velocity (\( v \)), distance (\( d \)), and time (\( t \)) is expressed with the formula:
\[ v = \dfrac{d}{t} \]
where:
- \( v \) is the velocity in meters per second (\(\text{m/s}\)).
- \( d \) is the distance in meters (\(\text{m}\)).
- \( t \) is the time in seconds (\(\text{s}\)).
Example 1: Finding the Velocity of a Moving Car
Given:
- Distance (\( d \)) = \( 300 \, \text{m} \)
- Time (\( t \)) = \( 20 \, \text{s} \)
Step-by-Step Calculation:
Step 1: Substitute the Values into the Velocity Formula
\[ v = \dfrac{d}{t} \]
\[ v = \dfrac{300}{20} \]
Step 2: Perform the Division
\[ v = 15 \]
Final Value
The velocity of the car is:
\[ v = 15 \, \text{m/s} \]
Example 2: Determining the Velocity of a Runner
Given:
- Distance (\( d \)) = \( 240 \, \text{m} \)
- Time (\( t \)) = \( 30 \, \text{s} \)
Step-by-Step Calculation:
Step 1: Substitute the Values into the Velocity Formula
\[ v = \dfrac{d}{t} \]
\[ v = \dfrac{240}{30} \]
Step 2: Perform the Division
\[ v = 8 \]
Final Value
The velocity of the runner is:
\[ v = 8 \, \text{m/s} \]
Example 3: Calculating the Velocity of a Cyclist
Given:
- Distance (\( d \)) = \( 300 \, \text{m} \)
- Time (\( t \)) = \( 25 \, \text{s} \)
Step-by-Step Calculation:
Step 1: Substitute the Values into the Velocity Formula
\[ v = \dfrac{d}{t} \]
\[ v = \dfrac{300}{25} \]
Step 2: Perform the Division
\[ v = 12 \]
Final Value
The velocity of the cyclist is:
\[ v = 12 \, \text{m/s} \]
This formula is straightforward and useful for calculating velocity in various contexts, from everyday motion to scientific experiments.
