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.
Example 1: Finding Distance
A bus travels at \(50\ km/h\) for \(3\ hours\). How far does it travel?
\(Distance=Speed\times Time\)
\(Distance=50\times 3\)
\(Distance=150\ km\)
Example 2: Finding Time
A train travels \(240\ km\) at a speed of \(60\ km/h\). How much time does it take?
\(Time=\frac{Distance}{Speed}\)
\(Time=\frac{240}{60}\)
\(Time=4\ h\)
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.
Speedometer and Odometer:
Vehicles such as scooters, motorbikes, cars and buses have instruments that help us understand their motion.
Speedometer:
A speedometer is an instrument fitted in a vehicle that measures and displays the speed of the vehicle.
Its reading is commonly given in: \(km/h\)
For example, if a speedometer shows \(60\ km/h\), it tells the driver that the vehicle is moving at a speed of \(60\ kilometres\ per\ hour\) at that time.
Odometer:
An odometer is an instrument that measures the distance travelled by a vehicle.
Its reading is commonly given in: \(km\)
For example, if an odometer shows \(1250\ km\), it indicates the distance recorded by the vehicle.