Math resources Ratio and proportion

Compound measures

Speed formula

# Speed formula

Here you will learn about the speed formula including understanding and using the terms constant speed and average speed. You will also be calculating the average speed of an object given its distance and time. This will extend to using and applying the speed formula and solving problems involving the speed formula.

Students will first learn about the speed formula as part of ratios & proportional relationships in 6 th grade.

## What is the speed formula?

The speed formula is given by

Speed = distance \div time

“Speed equals distance divided by time”

You will normally shorten this to:

### What is speed?

Speed is about how fast an object moves. The speed of the moving object is found by calculating the relationship between the distance the object travels and the period of time taken to travel the distance.

Some examples of the units of speed are:

• Meters per second (m/s)
• Miles per hour (mph)
• Km per hour (km/h)

Some real life examples of speeds in a constant medium include:

• Speed of sound – 343\mathrm{~m/s}
• Speed of light – 299~792~458\mathrm{~m/s}

You can calculate the average speed of an object by dividing the total distance by the total time.

If you consider the direction of the movement as well as its speed, then this is called the object’s velocity, which refers to the instantaneous speed and direction of an object at a specific point in time.

### What is time?

Time can be defined as the ongoing sequence of events taking place.

Some examples of the units of time are:

• Seconds (sec)
• Minutes (mins)
• Hours (hrs)
• Days

Note: The SI unit (Standard Unit Measurement) for time is a second.

### What is distance?

Distance is the length of space between two points.

Some examples of the units of distance are:

• Millimeters (mm)
• Centimeters (cm)
• Meters (m)
• Kilometers (km)
• Miles

Note: if you only consider how far the object has moved in regard to its starting point this is called displacement.

### Rate of change

The speed of an object is the rate of change between the distance covered and the amount of time taken. When working with graphs, the rate of change can be found by calculating the gradient of the distance-time graph.

As a constant speed is where the speed does not change, a straight line on a distance-time graph indicates a constant speed as the rate of change is the same.

Step-by-step guide: Speed distance time

## Common Core State Standards

How does this relate to 6 th grade math?

• Grade 6 – Ratios & Proportional Relationships (6.RP.A.3)
Use ratio and rate reasoning to solve real-world and mathematical problems, for example, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

## How to use the speed formula

In order to use the speed formula:

1. Write down known variables and their units.
2. Check to see if the units need to be converted.
3. Write down the speed formula.
4. Solve to find speed (or distance or time).

## Speed formula examples

### Example 1: calculating speed by substituting values into the speed formula

A car travels at a constant speed. The car travels 100 miles in 2 hours. What is the speed of the car? Give your answer in miles per hour (mph).

1. Write down known variables and their units.

Speed: unknown

Distance: 100 miles

Time: 2 hours

2Check to see if the units need to be converted.

Units are correct as the units in the question are already in miles and hours.

3Write down the speed formula.

Speed = distance \div time or S=D\div{T}.

4Solve to find speed (or distance or time).

You are finding the speed.

\begin{aligned}S&=D\div{T} \\\\ &=100\div{2} \\\\ &=50 \end{aligned}

The distance in miles is being divided by the time in hours, so the units are miles per hour.

The car travels at 50\mathrm{~mph}.

### Example 2: calculating speed by substituting values into the speed formula

A train travels at a constant speed. The train travels a total distance of 450 \mathrm{~km} in a period of time of 4 hours. Give your answer in kilometers per hour (kmph).

Write down known variables and their units.

Check to see if the units need to be converted.

Write down the speed formula.

Solve to find speed (or distance or time).

### Example 3: calculating speed by substituting values into the speed formula with unit conversion

A person walks at a constant speed. They travel 600 meters in 0.25 hours. Give your answer in meters per minute (m/min).

Write down known variables and their units.

Check to see if the units need to be converted.

Write down the speed formula.

Solve to find speed (or distance or time).

### Example 4: using speed to find another value

Phil is running in a race. Phil runs at an average speed of 5\mathrm{~m/s}.

The race is 21\mathrm{~km} long. What is the amount of time Phil takes to finish the race?

Write down known variables and their units.

Check to see if the units need to be converted.

Write down the speed formula.

Solve to find speed (or distance or time).

### Example 5: using speed to find another value

Question: A train travels at 120\mathrm{~km/h} for 3\cfrac{1}{4} hours. Calculate the total distance traveled.

Write down known variables and their units.

Check to see if the units need to be converted.

Write down the speed formula.

Solve to find speed (or distance or time).

### Example 6: problem involving speed

Miss Yellow completes a journey in 3 stages.

In the first stage, she travels at 33.75\mathrm{~km} in 45 minutes.

In the second stage, she travels 258\mathrm{~km} in 4 hours and 18 minutes.

The final stage is much shorter and she travels 1200\mathrm{~m} in 90 seconds.

What was her average speed for the whole journey?

Write down known variables and their units.

Check to see if the units need to be converted.

Write down the speed formula.

Solve to find speed (or distance or time).

### Teaching tips for speed formula

• Incorporate real life examples for speed calculations such as driving a car, running races, or the speed of a cyclist to make the concept relatable.

• Include problems on worksheets where students need to find either distance or time given the other two variables.

• Provide solved examples followed by similar practice problems for students to solve on their own or solved examples with mistakes for students to use for error analysis.

• Emphasize the importance of a consistent unit of measurement (miles per hour, meters per second, etc.).

• Be sure students are solid on the definition of speed and the formula of speed and introduce related terms like speedometer.

### Easy mistakes to make

• Using an incorrect speed formula
You must remember the speed formula with the correct operations between distance and time.
Speed = Distance \div Time

• Not converting units when necessary
You must remember the relationship between the units is important for the context of the question. If you are given an object’s speed in km per hour and the time in minutes, you need to first convert one of the units to be able to give an answer in hours.
For example, km/h divided by minutes does not give you km.

If you have found that the average speed of a car is 300\mathrm{~mph}, you have most likely made an error, as this answer is not reasonable within the context of the question as it is too high speed for a car. This is a useful (and quick) way of checking your answer.

### Practice speed formula questions

1. Find the speed of an object which traveled 240\mathrm{~km/h} in 3 hours. Give your answer in km/h.

720\mathrm{~km/h}

80\mathrm{~km/h}

0.0125\mathrm{~km/h}

80,000\mathrm{~m/h}
S=240\div{3}=80\mathrm{~km}/h

2. Find the speed of an object which traveled 500\mathrm{~m} in 5 hours. Give your answer in m/h.

100\mathrm{~m/h}

2500\mathrm{~m/h}

0.01\mathrm{~m/h}

0.1\mathrm{~km/h}
S=500\div{5}=100\mathrm{~m}/h

3. Find the speed of an object which traveled 1200\mathrm{~m} in 3 hours. Give your answer in km/h.

400\mathrm{~m/h}

2500\mathrm{~m/h}

0.4\mathrm{~km/h}

2.5\mathrm{~km/h}
1200\mathrm{~m}=1.2\mathrm{~km}

Speed = Distance \div Time

S=1.2\div{3}=0.4\mathrm{~km/h}

4. A person walks at a constant speed. They travel 900\mathrm{~m} in 0.5 hours. Calculate the speed. Give your answer in meters per minute (m/min).

30\mathrm{~m/h}

1.8\mathrm{~m/min}

1800\mathrm{~m/min}

30\mathrm{~m/min}

To convert from hours to minutes, multiply by 60.

0.5\times{60}=30 minutes

Speed = Distance \div Time

S=900\div{30}=30\mathrm{~m/min}

5. A person walks at a constant speed of 3 miles per hour. They walk for 90 minutes. Calculate how far they walk.

270 miles

4.5 miles

9 miles

45 miles

To convert from minutes to hours, divide by 60.

90\div{60}=1.5 hours

Distance = Speed \times Time

D=3\times{1.5}=4.5 miles

6. An object travels 1800\mathrm{~m} at a speed of 6\mathrm{~m/s}. Calculate the time taken. Give your answer in minutes.

300 minutes

50 minutes

3 minutes

5 minutes

Time = Distance \div Speed

T=1800\div{6}=300 seconds.

300 seconds is 5 minutes.

## Speed formula FAQs

What is the speed formula?

The speed formula is Speed = Distance \div Time.

How is the speed formula similar to the time formula?

The speed formula (S=D\div{T}) and the time formula (T=D\div{S}) are similar because both are derived from the fundamental relationship between distance, speed, and time (Distance = Speed \times Time). They use the same variables, rearranged to solve for different quantities.

What is the difference between average speed and average velocity?

Average speed measures how fast an object travels over a distance without considering direction. It’s a scalar quantity. Average velocity includes both the speed and direction of an object’s motion over a period of time. It’s a vector quantity.

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