Knowing how long it will take to cover a given distance is a fundamental concept in physics and daily life. This can be calculated using the relationship between distance, velocity, and time. This article will guide you through determining the time required to cover a specific distance when the velocity is known.
Formula to Find Time
The time (\( t \)) to cover a distance (\( d \)) at a constant velocity (\( v \)) is given by rearranging the basic formula for velocity:
\[ v = \dfrac{d}{t} \]
Solving for \( t \), we get:
\[ t = \dfrac{d}{v} \]
where:
- \( t \) is the time in seconds (\(\text{s}\)).
- \( d \) is the distance in meters (\(\text{m}\)).
- \( v \) is the velocity in meters per second (\(\text{m/s}\)).
Example 1: Calculating Time for a Car Trip
Given:
- Distance (\( d \)) = \( 300 \, \text{m} \)
- Velocity (\( v \)) = \( 15 \, \text{m/s} \)
Step-by-Step Calculation:
Step 1: Substitute the Values into the Time Formula
\[ t = \dfrac{d}{v} \]
\[ t = \dfrac{300}{15} \]
Step 2: Perform the Division
\[ t = 20 \]
Final Value
The time required for the car to cover \( 300 \, \text{m} \) is:
\[ t = 20 \, \text{s} \]
Example 2: Finding Time for a Running Distance
Given:
- Distance (\( d \)) = \( 500 \, \text{m} \)
- Velocity (\( v \)) = \( 10 \, \text{m/s} \)
Step-by-Step Calculation:
Step 1: Substitute the Values into the Time Formula
\[ t = \dfrac{d}{v} \]
\[ t = \dfrac{500}{10} \]
Step 2: Perform the Division
\[ t = 50 \]
Final Value
The time required for the runner to cover \( 500 \, \text{m} \) is:
\[ t = 50 \, \text{s} \]
Example 3: Time Required for a Cycling Distance
Given:
- Distance (\( d \)) = \( 750 \, \text{m} \)
- Velocity (\( v \)) = \( 25 \, \text{m/s} \)
Step-by-Step Calculation:
Step 1: Substitute the Values into the Time Formula
\[ t = \dfrac{d}{v} \]
\[ t = \dfrac{750}{25} \]
Step 2: Perform the Division
\[ t = 30 \]
Final Value
The time required for the cyclist to cover \( 750 \, \text{m} \) is:
\[ t = 30 \, \text{s} \]
