Speed
A runner covers $100\ \text{m}$ in $20\ \text{s}$. A cyclist covers $30\ \text{km}$ in $2\ \text{h}$. Who is faster? To compare them you need a single quantity that relates how far they go to how long they take: speed.
What speed is
Two swimmers train in a pool: Regina swims $50\ \text{m}$ in $25\ \text{s}$ and Camila swims $100\ \text{m}$ in $60\ \text{s}$. They have covered different distances in different times. How can you tell who swims faster? You have to look at how much distance each one covers every second.
In 2nd-year Physics we distinguish between speed and velocity. Speed only tells you how fast you are moving (it is a number, with no direction). Velocity, which you will see in other sections, also has a direction. Here we only use speed.
Solving for distance and time
From $v = d/t$ you get two other forms, depending on which piece of data is missing:
$$d = v \cdot t \qquad\qquad t = \frac{d}{v}$$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.
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?
Converting units: m/s and km/h
On Mexican highways, speed limits are given in $\text{km/h}$ (for example, $110\ \text{km/h}$ on the freeway), but in Physics we usually work in $\text{m/s}$. You need to be able to go from one to the other.
Why $3.6$? Because $1\ \text{km} = 1000\ \text{m}$ and $1\ \text{h} = 3600\ \text{s}$, and $3600 \div 1000 = 3.6$.
If the data are given in other units, such as $\text{m/min}$, you convert using the same reasoning: $900\ \text{m/min}$ means $900\ \text{m}$ in $60\ \text{s}$, that is, $900 \div 60 = 15\ \text{m/s}$.
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 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.
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 trips with several legs
You leave Puebla heading for Mexico City: you drive for 1 hour on the highway at $120\ \text{km/h}$, but then you hit 2 hours of traffic at $20\ \text{km/h}$. What is your average speed? Is it the mean of $120$ and $20$?
To see why, first look at a different trip, with two legs of the same distance (60 km each); at the end we will come back to the traffic jam.
Watch out for stops: if you wait at a traffic light, that time also counts in the total time, even though you are not moving forward. That is why your average speed is lower than your speed while you are walking.
You also need to distinguish distance from displacement. If a swimmer crosses the pool and comes back to the starting point, the distance traveled is twice the length, but her displacement (how much her position changed between the start and the end) is zero. Average speed uses the distance traveled, not the displacement.
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: the runner goes at $5\ \text{m/s}$, which is $18\ \text{km/h}$. The cyclist goes at $30 \div 2 = 15\ \text{km/h}$. So the runner is faster. And on the traffic-jam trip you cover $120 + 40 = 160\ \text{km}$ in $3\ \text{h}$: an average speed of about $53\ \text{km/h}$, not $70\ \text{km/h}$.