Calculating the speed of a car when you know the time taken and the distance covered is a straightforward yet essential skill. This can be done using a basic algebraic formula. Let's explore how to find the speed of a car using various relatable examples.
Formula to Find Speed
The speed (\( v \)) of a car is determined by dividing the distance (\( d \)) by the time (\( t \)):
\[ v = \dfrac{d}{t} \]
where:
- \( v \) is the speed 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: Commuting to Work
Scenario: You drive to work, covering a distance of \( 12 \, \text{km} \) in \( 15 \, \text{minutes} \). What is your average speed?
Step-by-Step Calculation:
1. Convert Distance to Meters:
\[ 12 \, \text{km} = 12 \times 1000 = 12000 \, \text{m} \]
2. Convert Time to Seconds:
\[ 15 \, \text{minutes} = 15 \times 60 = 900 \, \text{s} \]
3. Substitute Values into the Speed Formula:
\[ v = \dfrac{d}{t} \]
\[ v = \dfrac{12000}{900} \]
4. Perform the Division:
\[ v = 13.33 \, \text{m/s} \]
Final Value
The average speed of the car is:
\[ v = 13.33 \, \text{m/s} \]
Example 2: Road Trip
Scenario: During a road trip, you drive \( 250 \, \text{km} \) in \( 4 \, \text{hours} \). What is your average speed?
Step-by-Step Calculation:
1. Convert Distance to Meters:
\[ 250 \, \text{km} = 250 \times 1000 = 250000 \, \text{m} \]
2. Convert Time to Seconds:
\[ 4 \, \text{hours} = 4 \times 3600 = 14400 \, \text{s} \]
3. Substitute Values into the Speed Formula:
\[ v = \dfrac{d}{t} \]
\[ v = \dfrac{250000}{14400} \]
4. Perform the Division:
\[ v = 17.36 \, \text{m/s} \]
Final Value
The average speed during the road trip is:
\[ v = 17.36 \, \text{m/s} \]
Example 3: Racing Event
Scenario: In a racing event, a car completes a \( 2.5 \, \text{km} \) lap in \( 2 \, \text{minutes} \). What is its average speed?
Step-by-Step Calculation:
1. Convert Distance to Meters:
\[ 2.5 \, \text{km} = 2.5 \times 1000 = 2500 \, \text{m} \]
2. Convert Time to Seconds:
\[ 2 \, \text{minutes} = 2 \times 60 = 120 \, \text{s} \]
3. Substitute Values into the Speed Formula:
\[ v = \dfrac{d}{t} \]
\[ v = \dfrac{2500}{120} \]
4. Perform the Division:
\[ v = 20.83 \, \text{m/s} \]
Final Value
The average speed of the car in the racing event is:
\[ v = 20.83 \, \text{m/s} \]
Summary
To find the speed of a car given the distance and time, use the formula:
\[ v = \dfrac{d}{t} \]
where:
- \( d \) is the distance.
- \( t \) is the time.
In the examples provided:
1. For a distance of \( 12 \, \text{km} \) covered in \( 15 \, \text{minutes} \), the speed is \( 13.33 \, \text{m/s} \).
2. For a distance of \( 250 \, \text{km} \) covered in \( 4 \, \text{hours} \), the speed is \( 17.36 \, \text{m/s} \).
3. For a distance of \( 2.5 \, \text{km} \) covered in \( 2 \, \text{minutes} \), the speed is \( 20.83 \, \text{m/s} \).
This formula is widely applicable, from daily commuting to participating in racing events.
