Speed
A cyclist on Reforma, a plane leaving Guadalajara, the sound of thunder on a rainy afternoon in Mexico City: they are all moving, 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
Ximena travels 100 m in 20 s and Diego travels 150 m in 35 s. Even though Diego went farther, who moved faster?
To find out, it is not enough to look at the distance or the time separately: you have to see how much distance is covered in each unit of time.
In this course we use "velocity" for motion in a straight line in one direction, as in these examples. When all that matters is how fast something moves, without its direction, we talk about speed (you saw it in MOVIMI-RAP). The numbers are the same here; velocity, however, can carry a sign depending on the direction, something we will come back to in CINE-MRU.
If you know the speed, you can also solve for the distance or the time:
$$d = v \cdot t \qquad\qquad t = \frac{d}{v}$$Why? If you advance $5\ \text{m}$ every second, in $20\ \text{s}$ you advance $5 \times 20 = 100\ \text{m}$. And to find how many seconds you need, you see how many times that speed fits into the distance.
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 $\text{m/s}$.
State which of the following expressions are units of speed and which are not, and explain why: a) $\text{m/s}$ b) $\text{kg/m}^3$ c) $\text{km/h}$ d) $\text{m/s}^2$
State which of the following expressions are units of speed and which are not, and explain why:
- a) $\text{m/s}$
- b) $\text{kg/m}^3$
- c) $\text{km/h}$
- d) $\text{m/s}^2$
A velociraptor runs at $10\ \text{m/s}$. What distance does it cover in $45\ \text{s}$ if it maintains that speed?
A velociraptor runs at $10\ \text{m/s}$. What distance does it cover in $45\ \text{s}$ if it maintains that speed?
How long does a lorry take to cover $200\ \text{km}$ if it travels at a constant speed of $80\ \text{km/h}$? Express the result in hours, and in hours and minutes.
How long does a lorry take to cover $200\ \text{km}$ if it travels at a constant speed of $80\ \text{km/h}$? Express the result in hours, and in hours and minutes.
Converting units: m/s and km/h
On federal highway signs you will see km/h; on a track, m/s. To compare, you have to use the same unit.
Why 3.6? A kilometer is $1000\ \text{m}$ and an hour is $3600\ \text{s}$; dividing $3600 \div 1000$ gives $3.6$.
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?
Order the following speeds from fastest to slowest, first expressing all of them in $\text{km/h}$: a) $25\ \text{m/s}$ b) $100\ \text{km/h}$ c) $1\ \text{km/min}$
Order the following speeds from fastest to slowest, first expressing all of them in $\text{km/h}$:
- a) $25\ \text{m/s}$
- b) $100\ \text{km/h}$
- c) $1\ \text{km/min}$
Average speed on trips with several legs
A truck travels 10 km on the highway at 100 km/h and takes 6 minutes. Then it travels another 10 km in heavy traffic at 25 km/h and takes 24 minutes. Both legs are the same length; why isn't the average speed for the whole trip halfway between 100 and 25?
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 $\text{km/h}$.
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 journey.
- c) Explain why the average speed is not $75\ \text{km/h}$, the mean of the two speeds.
A family takes a $300\ \text{km}$ road trip by car. They want to take $4\ \text{h}$ in total. After $2\ \text{h}$ of driving, they have covered $150\ \text{km}$. a) What…
A family takes a $300\ \text{km}$ road trip by car. They want to take $4\ \text{h}$ in total. After $2\ \text{h}$ of driving, they have covered $150\ \text{km}$.
- a) What is their average speed so far?
- b) What average speed must they maintain over the remaining distance to arrive on time?
Approaching, crossing paths, and the sound of thunder
Why? If one advances $20\ \text{km}$ in an hour and the other $10\ \text{km}$ toward it, together they "eat up" $30\ \text{km}$ of the distance in that hour.
Sound also travels at a known speed, about $340\ \text{m/s}$ in air. The light from the lightning bolt arrives almost instantly, so the delay of the thunder lets you calculate how far away it struck.
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: the cyclist goes about $5\ \text{m/s}$ ($18\ \text{km/h}$), a commercial airplane about $250\ \text{m/s}$ ($900\ \text{km/h}$), and the sound of thunder $340\ \text{m/s}$ ($1{,}224\ \text{km/h}$), the fastest of the three.