Relationship Between Speed, Distance and Time:
We know that speed tells us how fast an object is moving. When we know the distance travelled by an object and the time taken to cover that distance, we can calculate its speed.
\(Speed = \frac{Total\ distance\ covered}{Total\ time\ taken}\)
For example, if a car covers \(120\ km\) in \(2\ hours\):
\(Speed = \frac{120}{2}\)
\(Speed = 60\ km/h\)
Therefore, the car's speed is \(60\ km/h\).
The relationship between these three quantities can be written in three forms:
| Quantity to find | Formula |
|---|---|
| Speed | \(Speed=\frac{Distance}{Time}\) |
| Distance | \(Distance=Speed\times Time\) |
| Time | \(Time=\frac{Distance}{Speed}\) |
These formulas help us calculate any one quantity when the other two quantities are known.
Unit conversion:
To convert km/h into m/s, multiply the value by 1000 and divide it twice by 60 or multiply the value by 5/18.
Example: Convert \(54\ km/h\) to \(m/s\)
\(75\ km/h\ =\ \frac{54 \times 1000}{3600}\)
\(=\ \frac{54 \times 5}{18}\)
\(=\ 15\ m/s\)
To convert m/s into km/h, multiply it twice by 60 and divide by 1000 or multiply the value by 18/5.
Example: Convert \(70\ m/s\) to \(km/hr\)
\(70\ m/s\ =\ \frac{70 \times 3600}{1000}\)
\(=\ \frac{70\ \times 18}{5}\)
\(=\ 252\ km/hr\)
Example 1: Finding Distance
A bus travels at \(50\ km/h\) for \(3\ hours\). How far does it travel?
\(Distance=Speed\times Time\)
\(Distance=50\times 3\)
\(Distance=150\ km\)
Average Speed:
In real life, an object usually does not move at the same speed throughout its journey. For example, a bus may move faster on an open road, slow down in traffic, and stop at a bus stop.
When the speed changes during a journey, we can calculate the average speed for the entire journey.
\(Average\ speed = \frac{Total\ distance}{Total\ time}\)
\(SI unit\ =\ \frac{m}{s}\)
Example:
A car travels \(100\ km\) in \(2\ hours\) and then travels another \(150\ km\) in \(3\ hours\).
Step 1: Find total distance
\(100+150=250\ km\)
Step 2: Find total time
\(2+3=5\ h\)
Step 3: Find average speed
\(Average\ speed = \frac{250}{5}\)
\(Average\ speed = 50\ km/h\)
Therefore, the average speed of the car for the entire journey is \(50\ km/h\).
Average speed is not always the simple average of the different speeds. We calculate it using:
\(Total\ distance\div Total\ time\)
When we use the word speed for a complete journey, it refers to the average speed calculated from the total distance and total time.