Speed
A cyclist, an airplane, 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 traveled to the time taken. That quantity is speed.
What speed is
Two athletes are training on a track: Emma runs 100 m in 20 s and Jayden runs 150 m in 35 s; although Jayden has gone farther, who has moved faster?
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 $\text{m/s}$.
A commuter train covers $240\ \text{km}$ in $2\ \text{h}$. What was its speed? Express it in $\text{km/h}$.
A commuter train covers $240\ \text{km}$ in $2\ \text{h}$. What was its speed? Express it in $\text{km/h}$.
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 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 $\text{km/h}$?
Changing units: m/s and km/h
On a US highway a car goes 65 mph. In the lab you use SI units, so you need to switch units: how fast is 65 mph in m/s?
A car travels at $90\ \text{km/h}$. Express its speed in $\text{m/s}$.
A car travels at $90\ \text{km/h}$. Express its speed in $\text{m/s}$.
An athlete runs at $15\ \text{m/s}$. Express their speed in $\text{km/h}$.
An athlete runs at $15\ \text{m/s}$. Express their speed in $\text{km/h}$.
How many meters does an electric scooter traveling at $18\ \text{km/h}$ cover in one minute?
How many meters does an electric scooter traveling at $18\ \text{km/h}$ cover in one minute?
Average speed on trips with several legs
A bus travels 10 miles on the interstate at 60 mph in 10 minutes, but then takes 40 minutes to cover another 10 miles in a traffic jam at 15 mph: if the two legs of the trip are the same length, why is the average speed for the whole trip not halfway between 60 and 15?
A cyclist covers $30\ \text{km}$ in the first hour of a ride and another $30\ \text{km}$ in the following half hour. Calculate their average speed over the whole trip,…
A cyclist covers $30\ \text{km}$ in the first hour of a ride and another $30\ \text{km}$ in the following half hour. Calculate their average speed over the whole trip, in $\text{km/h}$.
An intercity bus covers $180\ \text{km}$ in $2\ \text{h}\ 15\ \text{min}$. What was its average speed in $\text{km/h}$?
An intercity bus covers $180\ \text{km}$ in $2\ \text{h}\ 15\ \text{min}$. What was its average speed 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 trip.
- 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
During a summer storm in Houston you see a flash and count the seconds until the boom. How far away is the lightning?
Sound also travels at a known speed, about $340\ \text{m/s}$ in air (343 m/s at 20 °C): that is why you can work out how far away lightning struck by measuring how long the thunder takes to arrive. This is the "flash-to-bang" rule: light arrives almost instantly, so the delay is the sound's travel time. Sound covers about 1 mile in 5 seconds.
Sound travels through the air at about $340\ \text{m/s}$. You see lightning strike and hear the thunder $5\ \text{s}$ later, as shown in the figure. How far away from…
Sound travels through the air at about $340\ \text{m/s}$. You see lightning strike and hear the thunder $5\ \text{s}$ later, as shown in the figure.
How far away from you did the lightning strike?
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 toward the other's town, as shown in the figure.
- a) How many kilometers 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 $5\ \text{m/s}$ (about 11 mph), a commercial airplane at about $250\ \text{m/s}$ (about 560 mph) and the sound of thunder travels at $340\ \text{m/s}$ (about 760 mph), the fastest of the three.