A cyclist, an aeroplane, the sound of thunder: they all move, but at very different rates. To compare how fast each one goes, you need a quantity that relates the distance travelled to the time taken. That quantity is speed.
Before you start, make sure you know: Converting units (2nd ESO)
Two athletes are training on a track: Marta runs 100 m in 20 s and David runs 150 m in 35 s; although David has gone further, who has moved more quickly?
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A cyclist covers $100\ \text{m}$ in $20\ \text{s}$. At what speed did they travel? Express the result in $\text{m/s}$.
A cyclist covers $100\ \text{m}$ in $20\ \text{s}$. At what speed did they travel? Express the result in $\text{m/s}$.
Who moves faster: a runner covering $100\ \text{m}$ in $12\ \text{s}$ or a swimmer covering $50\ \text{m}$ in $25\ \text{s}$? Calculate the speed of each and compare…
Who moves faster: a runner covering $100\ \text{m}$ in $12\ \text{s}$ or a swimmer covering $50\ \text{m}$ in $25\ \text{s}$? Calculate the speed of each and compare them.
A bus travels 10 km along a dual carriageway at 100 km/h in 6 minutes, but then takes 24 minutes to cover another 10 km in a traffic jam at 25 km/h: if the two stages are the same length, why is the average speed for the whole journey not halfway between 100 and 25?
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A cyclist covers $30\ \text{km}$ in the first hour of a ride and another $30\ \text{km}$ in the following half an hour. Calculate their average speed over the whole…
A cyclist covers $30\ \text{km}$ in the first hour of a ride and another $30\ \text{km}$ in the following half an hour. Calculate their average speed over the whole journey, in $\text{km/h}$.
A car covers $100\ \text{km}$ at $100\ \text{km/h}$ and another $100\ \text{km}$ at $50\ \text{km/h}$, as shown in the figure. a) Calculate the time it takes for each…
A car covers $100\ \text{km}$ at $100\ \text{km/h}$ and another $100\ \text{km}$ at $50\ \text{km/h}$, as shown in the figure.
a) Calculate the time it takes for each section.
b) Calculate the average speed for the whole journey.
c) Explain why the average speed is not $75\ \text{km/h}$, the mean of the two speeds.
Approaching, passing each other and the sound of thunder
Sound also travels at a known speed, $340\ \text{m/s}$ in air: that is why you can work out how far away lightning struck by measuring how long the thunder takes to arrive.
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A commercial airliner covers $900\ \text{km}$ in $1,5\ \text{h}$. What is its speed in $\text{km/h}$?
A commercial airliner covers $900\ \text{km}$ in $1,5\ \text{h}$. What is its speed in $\text{km/h}$?
During a storm you hear thunder $3\ \text{s}$ after seeing the lightning strike. Sound travels through the air at $340\ \text{m/s}$. a) How far away from you did the…
During a storm you hear thunder $3\ \text{s}$ after seeing the lightning strike. Sound travels through the air at $340\ \text{m/s}$.
a) How far away from you did the lightning strike occur?
b) If during the next strike the thunder takes $10\ \text{s}$, is the storm approaching or moving away? Justify your answer with a calculation.
Two towns are $30\ \text{km}$ apart. A cyclist leaves the first town at $20\ \text{km/h}$ and, at the same time, another leaves the second town at $10\ \text{km/h}$,…
Two towns are $30\ \text{km}$ apart. A cyclist leaves the first town at $20\ \text{km/h}$ and, at the same time, another leaves the second town at $10\ \text{km/h}$, each heading towards the other's town, as shown in the figure.
a) How many kilometres closer to each other do they get every hour?
b) How long does it take for them to meet?
c) At what distance from the first town do they meet?
Back to the beginning: If you compare their speeds in $\text{m/s}$, the cyclist goes at about $5\ \text{m/s}$ ($18\ \text{km/h}$), a commercial aeroplane at about $250\ \text{m/s}$ ($900\ \text{km/h}$) and the sound of thunder travels at $340\ \text{m/s}$ ($1224\ \text{km/h}$), the fastest of the three.
Summary
Let's practice! 8 medium exercises in this section