Yaritza rides a bus on the Duarte Highway, a plane flies over the Cibao, and the sound of thunder rumbles over Santiago: they are all moving, but at very different paces. To compare how fast each one is going, you need a quantity that relates how far something goes to the time it takes. That quantity is velocity.
What velocity is
Two athletes train on a track: Starling covers 100 m in 20 s and Wilkin covers 150 m in 35 s. Even though Wilkin went farther, who moved faster?
Velocity tells you the distance a body covers in each unit of time. Starling: $100/20 = 5\ \text{m/s}$. Wilkin: $150/35 \approx 4.3\ \text{m/s}$. Starling moved faster, even though he did not go as far.
Practice★☆☆Not started
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 $\text{m/s}$.
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.
To change units, you multiply by conversion factors: fractions that equal 1 because the top and bottom have the same quantity in different units (for example, $\frac{1000\ \text{m}}{1\ \text{km}}$). You place the unit you want to remove so that it cancels out.
The reason: 1 km is 1,000 m and 1 h is 3,600 s; the quotient of 3,600 divided by 1,000 gives 3.6.
Practice★★☆Not started
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 $\text{m/s}$.
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 bus travels 10 km of highway 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 legs are the same length, why is the average velocity of the whole trip not halfway between 100 and 25?
Practice★★☆Not started
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.
Why: in one hour, one covers part of the way and the other covers another part; the distance shrinks by the sum of both.
Sound also travels at a known velocity, $340\ \text{m/s}$ in air. That's why you can calculate how far away lightning struck by measuring how long the thunder takes to arrive (light arrives almost instantly).
Practice★☆☆Not started
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 $\text{km/h}$?
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.
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: in $\text{m/s}$, the bus goes at about $25\ \text{m/s}$ ($90\ \text{km/h}$), a commercial plane at about $250\ \text{m/s}$ ($900\ \text{km/h}$), and the sound of thunder at $340\ \text{m/s}$ ($1{,}224\ \text{km/h}$), the fastest of the three.
Summary
Let's practice! 8 medium exercises in this section