## What you need to know

### Speed Distance Time

Speed is a measure of quickly something moves, so it is calculated by dividing distance by time.

\text{speed } = \dfrac{\text{distance}}{\text{time}}

Typically, we measure distance in metres (m), kilometres (km), or miles (sometimes also ‘m’, but it should always be clear in the question whether it’s metres or miles), and we measure time in seconds (s) or hours (h). As a result, the units we used to measure speed are compound units (for more information, see here conversions revision).

A good knowledge of how speed, distance, and time are related is important not only for when working with distance-time graphs (distance time graphs revision) and velocity-time graphs (velocity time graphs revision)

**Note:** The most common mistake made by students is always to do with units.

### Speed Distance Time Triangle

For most students, using a speed, distance and time triangle makes this subject easier. See the speed, distance, time triangle below.

### Example 1: Calculating Speed

A truck travels 110 miles in 2 hours. What is the average speed of the bus?

Speed is equal to the distance divided by the time, so this will be our calculation, but what will the unit of our answer be? In the question, the distance is given in miles and the time in hours, so the speed should be in miles per hour, which is denoted here like \text{m/h}.

\text{Speed } = \dfrac{110}{2} = 55\text{ m/h}

### Example 2: Calculating Distance

Jesse throws a ball that moves at an average speed of 35 metres per second and travels for a total of 4.5 seconds. Work out the distance travelled by the ball.

We’re looking for distance, so, constructing the triangle and covering up the d, we get

Therefore, to calculate the distance we must multiply the speed by the time. So

\text{distance }=35\times 4.5=157.5\text{ s}

### Example 3: Calculating Time

A car travels at an average speed of 50 mph. How long will it take for the car to travel 12.5 miles? Give your answer in minutes.

This time we cover up time

\text{Time } = \dfrac{12.5}{50} = 0.25\text{ m/h}

0.25 hours now needs to be converted into minutes by multiplying by 60

\text{Time }=0.25\times 60=15\text{ minutes}

### Example Questions

1) Skyler runs a new personal best in the 100-metre sprint. Her average speed over the course of the race is 8.5 metres per second. How long, to 2 decimal places, does it take her to run the race?

We are calculating the time taken, so by covering up the t we can see from the triangle above that we have to divide distance, d, by speed, s.

Therefore:

\text{time }=\dfrac{d}{s}=\dfrac{100}{8.5}=11.76\text{ seconds (2 decimal places)}

2) Gustavo is driving a bus along a motorway with a speed limit of 70 miles per hour. In 30 minutes, he travels 36 miles. Is his average speed during this period exceeding the speed limit?

We are calculating speed, so by covering up the s we can see from the triangle above that we have to divide distance, d, by time, t.

However, before we do that, we have to ensure that the units match. The speed limit is in ‘miles per **hour**’, but the time we have been given is in **‘minutes**’. This is easy, as 30 minutes is half an hour, or 0.5 hours. So, Gustavo’s average speed can be calculated as follows:

\text{speed }=\dfrac{d}{t}=\dfrac{36}{0.5}=72\text{ miles per hour}

So, **yes**, Gustavo is exceeding the speed limit.

3) On the first part of a journey, a motorcyclist travels for 3 hours at an average speed of 55 miles per hour.

On the second part of a journey, the same motorcyclist travels for 90 minutes at an average speed of 48 miles per hour.

How far does the motorcyclist travel in total?

In order to calculate the total distance travelled, we need to rearrange the speed / distance / time formula.

Since

\text{ speed} = \text{ distance} \div \text{ time}

then

\text{ distance} = \text{ speed} \times \text{ time}

The distance of the first part of the journey can be calculated as follows:

3 \text{ hours} \times 55 = 165 \text{ miles}

For the second part of the journey, we need to convert the units so that they match. The speed has been given in miles per *hour* whereas the time has been given in *minutes*. We can either convert the minutes into hours or we can convert the speed form miles per hour to miles per minute. Converting minutes to hours is probably the easier option.

90 \text{ minutes} = 1\frac{1}{2}\text{ hours or} 1.5\text{ hours}

The distance of the second part of the journey can be calculated as follows:

1.5 \text{ hours} \times 48 = \text{ 72 miles}

Therefore the total distance travelled is 165 + 72 = 37 \text{ miles}

4) The distance from the Sun to Mars is approximately 210 million kilometres. What is the speed of light in kilometres per second if it takes 11 minutes and 40 seconds for light to reach Mars from the Sun?

We know that to calculate speed, we need to divide distance by time as per the formula:

\text{ speed} = \text{ distance} \div \text{ time}

The only issue we have in this question is that the distance has been written as ‘210 million’, which is not that helpful as ‘million’ has been written as a word and not in figures. The first thing we will need to do is convert 210 million into figures, hopefully remembering that a million has 6 zeros.

210 million = 210,000,000

The time taken has been expressed in minutes and seconds which causes an additional problem. We have been asked to give an answer in kilometres per second, so we need to convert the time from minutes and seconds to seconds.

11 \text{ minutes} = 11 \times 60 \text{ seconds} = 660 \text{ seconds}

660 \text{ seconds} + 40 \text{ seconds} = 700 \text{ seconds}

We are now in a position to calculate the speed of light as follows:

\text{ Speed of light} = 210,000,000 \text{ km} \div 700 \text{ seconds} = 300,000\text{ m/s}

**Question 5:** Voyager 1 became the first spacecraft to leave the solar system after 35 years of space travel. Given that it is traveling at a speed of 17 \text{km/s}, work out an approximation for the size of the solar system. Give your answer in standard form.

We know that to calculate distance, we need to multiply speed by time as per the formula:

\text{ speed} = \text{ distance} \div \text{ time}

Hence converting 35 years to seconds

35 \text{ years} =35\times365\times24\times60\times60=1.104\times10^9 \text{ seconds}

The calculation becomes,

\text{ distance} = 17 \times 1.104\times10^9 =1.88\times10^{10}\text{ km}

### Worksheets and Exam Questions

#### (NEW) Speed Distance Time Exam Style Questions - MME

Level 4-5#### Speed Distance Time - Drill Questions

Level 4-5#### Speed and Density - Drill Questions

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