What speed is

Speed describes how fast something is moving. It measures the rate at which an object's distance changes over time. This concept helps us understand movement in everyday situations, like how quickly a car travels or a person runs.

Key features of speed

• Rate of change - Speed shows how much distance is covered in a given amount of time
• Scalar quantity - It only considers the magnitude of movement, not the direction
• Common examples - A slow walk might be 5 km/h, while a fast car could reach 100 km/h

Units of speed

Speed is measured in units that combine distance and time. The choice of unit depends on the context, such as short distances or long trips.

Common units for speed:

• Meters per second (m/s) - Used for short distances and precise measurements, like in science experiments
• Kilometers per hour (km/h) - Common for vehicles and longer distances, such as highway speeds
• Miles per hour (mph) - Often used in some countries for road speeds, like 55 mph on a freeway

Calculating speed

Speed can be calculated using a simple formula that relates distance and time. This allows us to find out how fast something moved after knowing how far it went and how long it took.

Formula for speed

$\text{Speed}=\frac{\text{distance}}{\text{time}}$

Where:

• Speed = Rate of movement (e.g., m/s, km/h, or mph)
• Distance = How far something travels (e.g., meters, kilometers, or miles)
• Time = Duration of the movement (e.g., seconds, minutes, or hours)

This formula works as long as the units for distance and time match the desired speed unit.

Worked example - Calculating speed in m/s

An object travels 200 metres in 40 seconds. Calculate its speed in meters per second.

Step 1: Identify the values

• Distance = 200 meters
• Time = 40 seconds

Step 2: Apply the formula

$\text{Speed}=\frac{\text{distance}}{\text{time}}$

Step 3: Substitution and calculation

$\text{Speed}=\frac{200}{40}=5\text{ m/s}$

The object's speed is 5 m/s.

Worked example - Calculating speed in km/h

A car covers 120 kilometers in 2 hours. Calculate its speed in kilometers per hour.

Step 1: Identify the values

• Distance = 120 kilometers
• Time = 2 hours

Step 2: Apply the formula

$\text{Speed}=\frac{\text{distance}}{\text{time}}$

Step 3: Substitution and calculation

$\text{Speed}=\frac{120}{2}=60\text{ km/h}$

The car's speed is 60 km/h.

Converting units for speed calculations

When calculating speed, the units for distance and time must be consistent. Conversions help match these units, using basic relationships between measurements. This ensures accurate results, especially when switching between small and large scales.

Key conversion factors

• Distance - 1 kilometer = 1,000 meters
• Time - 1 minute = 60 seconds
• Time - 1 hour = 3,600 seconds (since 60 minutes × 60 seconds = 3,600)

For example, to convert meters to kilometers, divide by 1,000. To convert seconds to hours, divide by 3,600.

Worked example - Converting units to calculate speed in km/h

A runner travels 5,000 meters in 1,800 seconds. Calculate the speed in kilometers per hour.

Step 1: Convert units

• Distance: 5,000 meters ÷ 1,000 = 5 kilometers
• Time: 1,800 seconds ÷ 3,600 = 0.5 hours

Step 2: Apply the formula

$\text{Speed}=\frac{\text{distance}}{\text{time}}$

Step 3: Substitution and calculation

$\text{Speed}=\frac{5}{0.5}=10\text{ km/h}$

The runner's speed is 10 km/h.

Worked example - Converting units to calculate speed in m/s

A vehicle moves 18 kilometers in 30 minutes. Calculate the speed in meters per second.

Step 1: Convert units

• Distance: 18 kilometers × 1,000 = 18,000 meters
• Time: 30 minutes × 60 = 1,800 seconds

Step 2: Apply the formula

$\text{Speed}=\frac{\text{distance}}{\text{time}}$

Step 3: Substitution and calculation

$\text{Speed}=\frac{\mathrm{18,000}}{\mathrm{1,800}}=10\text{ m/s}$

The vehicle's speed is 10 m/s.