Speed
On sports day, Aoife runs 100 m in 20 s. Her cousin Conor cycles 30 km in 2 h on the road out of Killarney. Who is faster? To compare them, you need a single quantity that relates the distance they cover to the time they take: speed.
What speed is
Two swimmers train in a pool: the first swims 50 m in 25 s and the second swims 100 m in 60 s; how can we tell for certain which one swims faster if they have covered different distances in different times?
In words: speed = distance ÷ time. Speed in a given direction is called velocity: 5 m/s to the north is a velocity.
A runner covers $100\ \text{m}$ in $20\ \text{s}$. Calculate their average speed in $\text{m/s}$.
A runner covers $100\ \text{m}$ in $20\ \text{s}$. Calculate their average speed in $\text{m/s}$.
State which of these expressions are units of speed and which are not, and explain why: a) $\text{m/s}$ b) $\text{km}$ c) $\text{km/h}$ d) $\text{s}$
State which of these expressions are units of speed and which are not, and explain why:
- a) $\text{m/s}$
- b) $\text{km}$
- c) $\text{km/h}$
- d) $\text{s}$
Who travels faster: Alma, who covers $60\ \text{m}$ in $12\ \text{s}$, or Bruno, who covers $40\ \text{m}$ in $10\ \text{s}$? Calculate the speed of each and compare…
Who travels faster: Alma, who covers $60\ \text{m}$ in $12\ \text{s}$, or Bruno, who covers $40\ \text{m}$ in $10\ \text{s}$? Calculate the speed of each and compare them.
Changing units: m/s and km/h
A car travels along a motorway at $90\ \text{km/h}$. Express its speed in $\text{m/s}$. Remember: $1\ \text{km} = 1000\ \text{m}$ and $1\ \text{h} = 3600\ \text{s}$.
A car travels along a motorway at $90\ \text{km/h}$. Express its speed in $\text{m/s}$. Remember: $1\ \text{km} = 1000\ \text{m}$ and $1\ \text{h} = 3600\ \text{s}$.
A greyhound runs at $20\ \text{m/s}$. Express its speed in $\text{km/h}$.
A greyhound runs at $20\ \text{m/s}$. Express its speed in $\text{km/h}$.
The distance from the Earth to the Moon is $3.84\times10^{8}\ \text{m}$ and light travels at $3\times10^{8}\ \text{m/s}$. How long does it take for moonlight to reach…
The distance from the Earth to the Moon is $3.84\times10^{8}\ \text{m}$ and light travels at $3\times10^{8}\ \text{m/s}$. How long does it take for moonlight to reach us? Give the answer in seconds, to two decimal places.
Finding distance and time
You know the speed of a bus. How can you work out how far it goes in a given time, or how long a journey will take?
I walk at a constant speed of $2\ \text{m/s}$. How long does it take me to cover $10\ \text{m}$?
I walk at a constant speed of $2\ \text{m/s}$. How long does it take me to cover $10\ \text{m}$?
A falcon glides at $8\ \text{m/s}$ for $30\ \text{s}$. What distance does it cover in that time?
A falcon glides at $8\ \text{m/s}$ for $30\ \text{s}$. What distance does it cover in that time?
A train needs to travel the last $500\ \text{m}$ before the station and has $30\ \text{s}$ to arrive on time. It travels at $20\ \text{m/s}$. a) How long does it take to…
A train needs to travel the last $500\ \text{m}$ before the station and has $30\ \text{s}$ to arrive on time. It travels at $20\ \text{m/s}$.
- a) How long does it take to travel those $500\ \text{m}$?
- b) Will it arrive on time?
- c) By how many seconds does it arrive early or late?
Comparing speeds
Who is faster: a car travelling at $72\ \text{km/h}$ or a cyclist going downhill at $15\ \text{m/s}$? Convert both speeds to the same unit to compare them.
Who is faster: a car travelling at $72\ \text{km/h}$ or a cyclist going downhill at $15\ \text{m/s}$? Convert both speeds to the same unit to compare them.
Order the following speeds from lowest to highest, expressing them all in $\text{m/s}$ first: a) $18\ \text{km/h}$ b) $10\ \text{m/s}$ c) $900\ \text{m/min}$
Order the following speeds from lowest to highest, expressing them all in $\text{m/s}$ first:
- a) $18\ \text{km/h}$
- b) $10\ \text{m/s}$
- c) $900\ \text{m/min}$
Average speed on journeys with several stages
You drive for 30 minutes along a motorway at 120 km/h, then spend 90 minutes crawling in a traffic jam at 20 km/h: what is your overall average speed, and why is it not the simple average of the two figures (70 km/h)?
To see why, first look at a different journey, with two stages of the same distance (60 km each); we will come back to the traffic jam at the end.
A swimmer crosses a $25\ \text{m}$ pool in $10\ \text{s}$ and returns to the starting point in $15\ \text{s}$, as shown in the figure. a) What is the total distance…
A swimmer crosses a $25\ \text{m}$ pool in $10\ \text{s}$ and returns to the starting point in $15\ \text{s}$, as shown in the figure.
- a) What is the total distance covered and how much time did it take?
- b) What is her average speed for the whole journey?
- c) What was her total displacement? Explain the difference between displacement and distance.
A car travels $60\ \text{km}$ at $120\ \text{km/h}$ and another $60\ \text{km}$ at $60\ \text{km/h}$, as shown in the figure. a) Calculate the time taken for each…
A car travels $60\ \text{km}$ at $120\ \text{km/h}$ and another $60\ \text{km}$ at $60\ \text{km/h}$, as shown in the figure.
- a) Calculate the time taken for each section.
- b) Calculate the average speed for the whole trip.
- c) Explain why the average speed is not $90\ \text{km/h}$, the mean of the two speeds.
A cyclist covers $3\ \text{km}$ in $10\ \text{min}$ with a tailwind and takes $15\ \text{min}$ to return along the same route. a) Calculate her speed on the outward and…
A cyclist covers $3\ \text{km}$ in $10\ \text{min}$ with a tailwind and takes $15\ \text{min}$ to return along the same route.
- a) Calculate her speed on the outward and return journeys, in $\text{km/h}$.
- b) Calculate her average speed for the complete trip.
- c) Is the average speed equal to the mean of the two speeds from part a)? Reason your answer.
Back to the beginning: Aoife's speed is $5\text{ m/s}$ ($18\text{ km/h}$) and Conor's is $15\text{ km/h}$ ($30\text{ km} \div 2\text{ h}$); therefore, Aoife is faster. And in the traffic-jam trip you cover $60 + 30 = 90\text{ km}$ in $2\text{ h}$, an average of $45\text{ km/h}$, not $70\text{ km/h}$.