3. Speed

Learning outcomes
  • I can define speed as the rate at which distance is traveled.
  • I can calculate speed using distance and time measurements.
  • I can identify the SI units used for speed.
  • I can distinguish between average speed and instantaneous speed.
  • I can solve problems involving speed, distance, and time.

Introduction

Imagine watching a race between a cyclist, a sprinter, and a racing car. Although they are all moving, they are clearly not moving at the same rate. To compare how quickly objects move, physicists use a quantity called speed.

Speed is one of the most common measurements used in everyday life. It tells us how fast a car is travelling, how quickly an athlete completes a race, or how long it will take to reach a destination. In physics, speed is closely linked to distance and time, making it one of the first mathematical concepts students encounter in the study of motion.

What is Speed?

Speed is the rate at which distance is travelled.

In other words, speed tells us how much distance an object travels in a given amount of time.

An object moving at a higher speed covers more distance in the same amount of time than an object moving at a lower speed.

Examples:

  • A walking person travels about 1.4 m/s.
  • A cyclist may travel at 8 m/s.
  • A car on a highway may travel at 100 km/h.
  • A commercial aircraft cruises at about 900 km/h.

Calculating Speed

Speed can be calculated if the distance travelled and the time taken are known.

\( v = \frac{d}{t} \)

\( v_{avg} = \frac{d}{t} = \frac{60}{5} = 12 \ m/s \)

The relationship between these quantities is:

\( Speed = \frac{distance}{time} \)

This formula can also be rearranged:

\( Time = \frac{Distance}{Speed} \)

These three equations are among the most frequently used in mechanics.

https://images.openai.com/static-rsc-4/B_oBek9jCA96Wa4_-F7g25G0sgI5XLlyQCEo3W8u8E5Jwpl_n8O744TkTY76l0TDBE1xg86xLKGFFGE2XvWzltUIk7yggW3DxcnDesZkc-kdErXNLu3thunFy0ctZZ7cbUt-BBqqjKQpdAsguHjLnnRnL7EGaQ8b-9zGhdlag_xjgPoNs4YWm1T31sR81XYe?purpose=fullsize

SI Units of Speed

The SI unit (International System of Units) for speed is:

metres per second (m/s)

This means the object travels a certain number of metres every second.

Examples:

  • 2 m/s means 2 metres every second.
  • 15 m/s means 15 metres every second.

Other common units include:

  • kilometres per hour (km/h)
  • centimetres per second (cm/s)
  • miles per hour (mph)

Scientists usually use m/s because it is the SI unit.

Example 1: Calculating Speed

A runner travels 100 m in 12.5 s.

Step 1

Write the known values.

Distance = 100 m

Time = 12.5 s

Step 2

Use the speed equation.

\( Speed = \frac{100}{12.5} \)

Step 3

Calculate.

Answer: The runner's speed is 8.0 m/s.

Average Speed

Average speed is the total distance travelled divided by the total time taken.

It describes the overall rate of motion during an entire journey.

Example:

A car travels:

  • 60 km in the first hour.
  • 40 km in the second hour.

Total distance:

Total time:

2 hours

Average speed:

\( \frac{100}{2} = 50 \ km/h \)

Although the car travelled at different speeds during the journey, its average speed was 50 km/h.

Instantaneous Speed

Instantaneous speed is the speed of an object at a particular moment in time.

It may change continuously during a journey.

Examples:

  • The speed shown on a car's speedometer.
  • A cyclist accelerating downhill.
  • A runner sprinting across the finish line.

Instantaneous speed tells us how fast an object is moving right now.

https://images.openai.com/static-rsc-4/PmgLLny38ralFjHhJGKnFjHB9nhZwSFOn9Kvcz8pxLEYwES7WL3vTJY1XmT_AgX4US1Qr3a6MMXoiGL_UG7SDgS2L60AkomQZLQxY5JY6yWR1cPweUq9M36XELQhH30cuYmbAB2p2WOEG6jIwOYuxlQTfPQlaBtA1P27KN8lYlm75MYHkm7lirN9rQbGZ7Ex?purpose=fullsize

Average Speed vs Instantaneous Speed

Average Speed  Instantaneous Speed
Calculated over an entire journey  Measured at one specific moment
Uses total distance and total time   Changes from moment to moment
Gives an overall rate of motion  Gives the speed at a particular instant

For journeys with changing speeds, the two values are often different.

Solving Speed, Distance, and Time Problems

Many motion problems involve finding one unknown quantity.

A simple strategy is:

Step 1

Identify the known quantities.

Step 2

Choose the correct equation.

Step 3

Substitute the values.

Step 4

Calculate the answer.

Step 5

Include the correct units.

Always check that:

  • Distance is measured in metres (or kilometres).
  • Time is measured in seconds (or hours).
  • Units are consistent before calculating.

Common Mistakes

Students often make these mistakes:

  • Mixing metres with hours.
  • Mixing kilometres with seconds.
  • Forgetting to include units.
  • Confusing distance with displacement.
  • Using the wrong equation.

Always convert units before solving problems.

Everyday Examples of Speed

Speed is measured in many situations.

Examples include:

  • Speed limits on roads.
  • Athletes running races.
  • Aircraft travelling between cities.
  • Ships crossing oceans.
  • Elevators moving between floors.
  • Internet data transfer (using a different definition of "speed").

Understanding speed helps us compare how quickly different objects move.

https://images.openai.com/static-rsc-4/KM2m2ndv6DO5_mzZqnfzTj0Me7JrRbM0wVhbxAMpxSvRrba-wJQRxPbEru-d2e8oUYRZM6relUkM36M1NgMsdiekl95HK3UEjg0dgqmSFl0NCJCmju55oDXLbp7da7w342Xi5uDzNI6nsT17Ds2eGEa58vAMNuiNYvjSIT--sTrfwdOo5MY6uQsiOJe1mVNv?purpose=fullsize

Why Understanding Speed is Important

Speed is one of the most important quantities in physics.

It allows scientists and engineers to:

  • Predict travel times.
  • Design safer roads.
  • Analyse sports performance.
  • Control robots and machines.
  • Plan aircraft and spacecraft trajectories.

Speed is also the foundation for understanding velocity and acceleration.

Real-World Connections

Speed measurements are used every day in science, engineering, and technology.

Examples include:

  • Police use radar guns to measure vehicle speeds.
  • Engineers test vehicle performance and safety.
  • Pilots monitor aircraft speed throughout a flight.
  • Sports scientists analyse athletes' running and cycling speeds.
  • Space agencies calculate spacecraft speeds during launches and planetary missions.

Accurate speed measurements help improve safety, efficiency, and performance.

Worked Example

A cyclist rides 18 km in 45 minutes.

Question

Calculate the cyclist's average speed in km/h.

Solution

Step 1

Convert the time.

45 minutes = 0.75 hours

Step 2

Use the equation.

\( Speed = \frac{18}{0.75} \)

Step 3

Calculate.

Answer: The cyclist's average speed is 24 km/h.

https://images.openai.com/static-rsc-4/nAZQevjVeLU0dbFZS_Yh76daDDBOURBQdQ5iUzF5366AL3yV5-SFYfuOxs1ouHbXipUBbOWrZumFS6jFERC5QRpXIXaZvRdTBrYTlRqneiFCArb5q1NqjYiBGVPOYRjbmcou3A4KL2Li2ldNJD684-JLQQngHmmH_AaDX-thglk7ZMfFnvfkbG3Fa9YQut-8?purpose=fullsize

Did You Know?

  • The fastest land animal, the cheetah, can reach speeds of about 110 km/h, but only for short distances.
  • The speed of sound in air at room temperature is approximately 343 m/s, while the speed of light in a vacuum is about 300 million m/s.
  • The International Space Station travels at about 28,000 km/h, allowing it to orbit Earth approximately every 90 minutes.

https://images.openai.com/static-rsc-4/HF4q2dOhIrwTEI5traPlcr5W-vP5OShYN7wGp9i_ryY_0OF-AAL-6lPhYLXw9BJz0QEA7mf-ZfAoOQYgHmbUUeK9K75O1z06S1OwyLQdC36H8aKo_I3gY11zxZxhTLM2o99EzcegO4RpQdhCzumnn3L3dThcug4vB25mksNt_0sb3nCh4Ozd6mQiwrzQGAlW?purpose=fullsize

https://images.openai.com/static-rsc-4/2oGkZscsoKV7HzckPhwyYBF-z7hGsi2nbOR0EN7iHxe-z4p0ALXFpGOgqYrmiHmPq_NuTZ6wcFTSNnd5IbQZHGZZ_JDxR2A61xi41L3Lxsgx2C9duVThZpb16mFVzuAzDraYJaG_smmSuwL763r87PUx0pKyPSODrhj4Hm1_egGcP6NDDwwIuOhOBNTr4UKa?purpose=fullsize

Key Terms

Speed — The rate at which distance is travelled.

Average Speed — The total distance travelled divided by the total time taken.

Instantaneous Speed — The speed of an object at a particular moment in time.

Distance — The total path travelled by an object.

Time — The duration over which motion occurs.

SI Unit — The standard international unit used for measurement. For speed, this is metres per second (m/s).

Key Takeaways

  • Speed measures how quickly distance is travelled.
  • Speed is calculated by dividing distance by time.
  • The SI unit of speed is metres per second (m/s), although km/h is also commonly used.
  • Average speed describes the overall rate of motion during a journey, while instantaneous speed describes the speed at a single moment.
  • Solving speed problems requires using consistent units and selecting the correct equation.
  • Understanding speed provides the foundation for studying velocity, acceleration, and more advanced concepts in mechanics.