Speed, Distance & Time Study Guide

Introduction

Speed, distance, and time are three closely related measurements used to describe motion. Whenever a car travels along a road, a runner completes a race, an aircraft flies between cities, or a spacecraft sends a signal through space, these quantities help us calculate how far something travels, how fast it moves, or how long the journey takes.

The basic relationship is simple:

Speed = Distance ÷ Time

From this equation, we can also calculate distance and time. NASA educational materials use the same rate relationship, commonly written as distance = speed × time.

Understanding speed, distance, and time is useful in mathematics, physics, transportation, sports, navigation, engineering, and everyday travel planning. It is also a common topic in school examinations and aptitude tests.

Learning Objectives

After studying this topic, you should be able to:

• Define speed, distance, and time.

• Use the three main speed-distance-time formulas.

• Choose suitable units for each quantity.

• Convert between common speed units.

• Calculate average speed correctly.

• Solve word problems involving journeys and motion.

What Are Speed, Distance, and Time?

Distance

Distance tells us how much ground an object has covered.

Common units of distance include:

• metres (m)

• kilometres (km)

• centimetres (cm)

• miles (mi)

In the International System of Units, or SI, the metre (m) is the base unit of length.

For example, if a cyclist travels from one town to another along a 24 km road, the distance travelled is 24 km.

Time

Time measures how long an event or journey lasts.

Common units include:

• seconds (s)

• minutes (min)

• hours (h)

The SI base unit of time is the second (s).

For example, if a train leaves at 2:00 p.m. and arrives at 4:30 p.m., its travel time is 2 hours 30 minutes.

Speed

Speed measures how much distance is travelled per unit of time.

For example, a car moving at 60 km/h travels 60 kilometres in one hour if it maintains that speed.

The coherent SI unit of speed is metres per second (m/s).

Other frequently used units include:

• kilometres per hour (km/h)

• miles per hour (mph or mi/h)

• metres per second (m/s)

The Speed, Distance and Time Formula

The three quantities are connected by one basic equation:

Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}

This can be rearranged to find distance or time.

These formulas are valid when the units are compatible. NASA's educational resources use the same distance-rate-time relationship.

Formula Triangle

A useful memory aid is the DST triangle:

       D

     -----

     S | T

Where:

• D = Distance

• S = Speed

• T = Time

Cover the quantity you want to calculate.

If you cover D, you are left with:

S × T

Therefore:

Distance = Speed × Time

If you cover S, you get:

D ÷ T

Therefore:

Speed = Distance ÷ Time

If you cover T, you get:

D ÷ S

Therefore:

Time = Distance ÷ Speed

How to Calculate Speed

Use:

Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}

Example 1

A bus travels 180 km in 3 hours. Find its average speed.

Speed=1803\text{Speed} = \frac{180}{3} Speed=60 km/h\text{Speed} = 60\text{ km/h}

Answer: 60 km/h

This means the bus covered an average of 60 kilometres during each hour of the journey.

Example 2

A runner completes 400 m in 50 seconds.

Speed=40050\text{Speed} = \frac{400}{50} Speed=8 m/s\text{Speed} = 8\text{ m/s}

Answer: 8 m/s

How to Calculate Distance

Use:

Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}

Example

A car travels at 70 km/h for 4 hours.

Distance=70×4\text{Distance} = 70 \times 4 Distance=280 km\text{Distance} = 280\text{ km}

Answer: 280 km

NASA uses this same relationship when explaining aircraft range: an aircraft travelling at constant ground speed covers a distance equal to its speed multiplied by its time aloft.

How to Calculate Time

Use:

Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}

Example

A cyclist needs to travel 90 km at an average speed of 30 km/h.

Time=9030\text{Time} = \frac{90}{30} Time=3 hours\text{Time} = 3\text{ hours}

Answer: 3 hours

Matching the Units

One of the most common mistakes in speed-distance-time problems is using incompatible units.

Suppose the distance is given in kilometres and speed is given in kilometres per hour. The resulting time will be in hours.

Similarly:

Always check the units before starting the calculation.

Converting Units of Time

Important time conversions include:

• 1 minute = 60 seconds

• 1 hour = 60 minutes

• 1 hour = 3,600 seconds

NIST lists an hour as equal to 3.6 × 10³ seconds, or 3,600 seconds.

Example

Convert 2.5 hours to minutes.

2.5×60=1502.5 \times 60 = 150

Answer: 150 minutes

Converting Speed Units

Different countries and fields use different speed units. Scientific calculations often use m/s, while road speeds are commonly expressed in km/h or mph.

NIST publishes standardized conversion factors for velocity and speed.

Quick Rule: km/h and m/s

To convert:

km/h → m/s: divide by 3.6

m/s → km/h: multiply by 3.6

Example

Convert 72 km/h to m/s.

72÷3.6=2072 \div 3.6 = 20

Answer: 20 m/s

Now convert 15 m/s to km/h.

15×3.6=5415 \times 3.6 = 54

Answer: 54 km/h

Average Speed

A vehicle does not always travel at the same speed throughout a journey. It may accelerate, slow down, stop at traffic lights, or encounter congestion.

For an entire journey:

Average Speed=Total Distance TravelledTotal Time Taken\text{Average Speed} = \frac{\text{Total Distance Travelled}} {\text{Total Time Taken}}

OpenStax describes average speed as the distance travelled divided by the time during which the motion occurs.

Example

A car travels:

• 120 km in 2 hours

• another 80 km in 1 hour

Total distance:

120+80=200 km120 + 80 = 200\text{ km}

Total time:

2+1=3 hours2 + 1 = 3\text{ hours}

Average speed:

2003=66.67 km/h\frac{200}{3} = 66.67\text{ km/h}

Answer: approximately 66.7 km/h

A Common Average-Speed Mistake

You should not usually calculate average speed by simply adding two speeds and dividing by two.

For example, if a vehicle travels part of its journey at 40 km/h and another part at 80 km/h, the average speed is not automatically 60 km/h.

The correct calculation depends on the total distance and total travel time.

Speed and Velocity: What is the Difference?

In everyday speech, speed and velocity are sometimes treated as the same thing. In physics, however, they have different meanings.

Speed tells us how fast an object moves.

Velocity includes both the rate of motion and its direction.

NASA describes velocity as a vector quantity because direction is required, while speed does not require a direction.

For example:

• 60 km/h describes speed.

• 60 km/h north describes velocity.

This distinction becomes important when studying more advanced topics such as vectors, acceleration, forces, and motion.

Real-World Applications

Travel Planning

Suppose a destination is 240 km away and you expect an average speed of 80 km/h.

240÷80=3240 \div 80 = 3

The journey would take approximately 3 hours, excluding additional stops or delays.

Sports

Speed calculations can compare performances in running, cycling, swimming, and motorsport.

If a runner covers 100 metres in 12.5 seconds:

100÷12.5=8 m/s100 \div 12.5 = 8\text{ m/s}

The runner's average speed is 8 m/s.

Aviation

Pilots and flight planners use speed, distance, and time when estimating travel duration and aircraft range. Under constant-speed conditions, NASA expresses aircraft range using the same relationship:

d=Vtd = Vt

where dd is distance, VV is speed, and tt is time.

Space Science

The same relationship can even be applied to electromagnetic signals travelling through space. The BIPM defines the speed of light in vacuum as exactly 299,792,458 m/s.

Scientists can use the travel time of a signal and its known speed to determine distance.

Multi-Step Word Problem

A coach travels 150 km at an average speed of 50 km/h, stops for 30 minutes, and then travels another 120 km at 60 km/h.

Step 1: Calculate the first travel time

150÷50=3 hours150 \div 50 = 3\text{ hours}

Step 2: Calculate the second travel time

120÷60=2 hours120 \div 60 = 2\text{ hours}

Step 3: Add the stop

30 minutes = 0.5 hours.

Total time:

3+0.5+2=5.5 hours3 + 0.5 + 2 = 5.5\text{ hours}

Total distance:

150+120=270 km150 + 120 = 270\text{ km}

Step 4: Calculate average speed for the complete trip

If the stop is included in the total journey time:

270÷5.5≈49.09 km/h270 \div 5.5 \approx 49.09\text{ km/h}

Average speed for the complete trip ≈ 49.1 km/h

This example shows why stops can significantly reduce the average speed calculated across an entire journey.

Common Mistakes

1. Mixing Hours and Minutes

If speed is given in km/h but time is given in minutes, convert the time before applying the formula.

For example:

30 minutes:

30÷60=0.5 hours30 \div 60 = 0.5\text{ hours}

2. Using the Wrong Formula

Remember:

• Find speed → D ÷ T

• Find distance → S × T

• Find time → D ÷ S

3. Forgetting Units

An answer such as 50 is incomplete.

Write:

50 km/h

or:

50 m/s

as appropriate.

4. Averaging Speeds Incorrectly

For a complete journey, calculate:

total distancetotal time\frac{\text{total distance}}{\text{total time}}

Do not automatically take the arithmetic mean of the individual speeds.

5. Including or Excluding Stops Incorrectly

Read the question carefully. Some problems ask for average speed while moving, while others ask for average speed over the entire journey, including stops.

Memory Tips

Remember the letters:

DST

• D = Distance

• S = Speed

• T = Time

The formulas are:

S=D/TS = D/T D=S×TD = S \times T T=D/ST = D/S

Another useful phrase is:

“Speed divides; distance multiplies.”

When finding speed or time, you divide. When finding distance, you multiply.

Summary

Speed, distance, and time describe how objects move and are connected by a simple mathematical relationship.

The central formula is:

Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}

From it, we get:

Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}

and:

Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}

Correct units are essential. Metres and seconds usually produce m/s, while kilometres and hours produce km/h. For journeys involving different speeds, average speed should generally be found using total distance divided by total time.

FAQ

1. What is the basic formula for speed?

The formula is:

Speed=Distance÷Time\text{Speed} = \text{Distance} \div \text{Time}

2. How do you calculate distance?

Multiply speed by time:

Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}

3. How do you calculate travel time?

Divide distance by speed:

Time=Distance÷Speed\text{Time} = \text{Distance} \div \text{Speed}

4. What is the SI unit of speed?

The SI coherent unit of speed is metres per second (m/s).

5. How do I convert km/h into m/s?

Divide the speed in km/h by 3.6.

For example:

90÷3.6=25 m/s90 \div 3.6 = 25\text{ m/s}

6. How do I convert m/s into km/h?

Multiply by 3.6.

For example:

10×3.6=36 km/h10 \times 3.6 = 36\text{ km/h}

7. Is speed the same as velocity?

Not exactly. Speed describes how fast an object moves, while velocity also specifies the direction of motion.

8. How is average speed calculated?

Use:

Average Speed=Total DistanceTotal Time\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}

9. Can an object's speed change during a journey?

Yes. A vehicle may speed up, slow down, or stop. Average speed summarizes the overall rate of travel across a chosen time interval.

10. Why must units match in speed calculations?

The units determine the meaning of the result. If distance is in kilometres and time is in hours, speed is measured in km/h. Mixing minutes, seconds, kilometres, and metres without conversion can produce an incorrect answer.

Key Takeaways

• Speed = Distance ÷ Time.

• Distance = Speed × Time.

• Time = Distance ÷ Speed.

• Always make distance, speed, and time units compatible before calculating.

• For a complete journey, average speed is normally total distance ÷ total time.

References

1. Bureau International des Poids et Mesures (BIPM) — SI Base Units. Defines the metre as the SI base unit of length and the second as the SI base unit of time. BIPM: SI Base Units

2. Bureau International des Poids et Mesures (BIPM) — SI Brochure. Authoritative reference for the International System of Units, including the SI treatment of speed and velocity. BIPM: SI Brochure

3. Bureau International des Poids et Mesures (BIPM) — Metre. Explains the SI definition of the metre and the defined value of the speed of light. BIPM: SI Unit Metre

4. National Institute of Standards and Technology (NIST) — Guide to the SI, Appendix B.9. Provides official conversion factors for time and velocity units, including km/h, m/s and mph. NIST: SI Conversion Factors

5. NASA Glenn Research Center — Aircraft Range: Constant Velocity. Demonstrates the distance-equals-speed-times-time relationship in aviation. NASA: Aircraft Range and Constant Velocity

6. NASA Glenn Research Center — Velocity. Explains the distinction between speed and velocity and the role of direction in velocity. NASA: Velocity Definition

7. OpenStax — Physics: Speed and Velocity. Educational reference covering average speed, instantaneous speed, distance, and time relationships. OpenStax: Speed and Velocity