Speed
Wilkin runs 100 m in 20 s on the school track. His cousin Yaritza rides her bike 30 km in 2 h along the Autopista Duarte. Who is faster? To compare them you need a single quantity that relates how far they go to the time they take: speed.
What speed is
Two swimmers are training in a pool: the first swims 50 m in 25 s and the second swims 100 m in 60 s. Since both the distances and the times are different, looking at just one piece of data is not enough. You have to see how much distance each one covers per unit of time.
If you know the speed, you can also solve for the distance or the time: $d = v \cdot t$ and $t = d/v$. For example, at $2\ \text{m/s}$ you cover $10\ \text{m}$ in $10 \div 2 = 5\ \text{s}$.
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 bus travels $150\ \text{km}$ at an average speed of $50\ \text{km/h}$. How long does it take to complete the journey?
A bus travels $150\ \text{km}$ at an average speed of $50\ \text{km/h}$. How long does it take to complete the journey?
Changing units: m/s and km/h
Cars and buses show their speed in km/h, but in Physical Science we almost always work in m/s. You need to know how to go from one to the other.
For other units (m/min, for example) go through seconds: $900\ \text{m/min} = 900\ \text{m} \div 60\ \text{s} = 15\ \text{m/s}$.
What does it mean for a car to travel at a speed of $20\ \text{m/s}$? Explain it with a sentence starting with "Every second...".
What does it mean for a car to travel at a speed of $20\ \text{m/s}$? Explain it with a sentence starting with "Every second...".
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 $\text{km/h}$.
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) $900\ \text{m/min}$
Ana walks to her training, which is $2\ \text{km}$ from home, at a speed of $4\ \text{km/h}$. Bea cycles to the sports center, which is $9\ \text{km}$ away, at…
Ana walks to her training, which is $2\ \text{km}$ from home, at a speed of $4\ \text{km/h}$. Bea cycles to the sports center, which is $9\ \text{km}$ away, at $12\ \text{km/h}$. They both leave at the same time.
- a) How long does each of them take?
- b) Express both times in minutes.
- c) Who arrives first?
Scientific notation with speed
Light travels at $300{,}000{,}000\ \text{m/s}$ and the Moon is $384{,}000{,}000\ \text{m}$ away. With so many zeros it is easy to make a mistake, which is why we use scientific notation: a number between 1 and 10 multiplied by a power of 10.
$$300{,}000{,}000 = 3\times10^{8} \qquad 384{,}000{,}000 = 3.84\times10^{8}$$The exponent is the number of places you move the decimal point to the right.
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.
Average speed on trips with several legs
You leave Santo Domingo heading for Santiago and drive for 1 hour on the highway at 120 km/h, but then you hit a traffic jam for 2 hours at 20 km/h. What was your average speed, and why is it not simply the average of the two figures?
To see it, 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.
Distance and displacement
Average speed uses the distance traveled, that is, the length of the path. If a swimmer swims 25 m out and 25 m back, she covered 50 m, but she ends up where she started: her displacement is 0 m. That is why average speed is not zero even though the displacement is.
Another useful case is that of a back-and-forth motion, like an echo: the sound travels the path twice, so the distance to the obstacle is half of what the sound travels. With $d = v \cdot t$ and the speed of sound ($340\ \text{m/s}$) you can calculate it.
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.
Bruno walks to school: he covers $400\ \text{m}$ in $4\ \text{min}$, waits $2\ \text{min}$ at a traffic light, and covers another $400\ \text{m}$ in $4\ \text{min}$, as…
Bruno walks to school: he covers $400\ \text{m}$ in $4\ \text{min}$, waits $2\ \text{min}$ at a traffic light, and covers another $400\ \text{m}$ in $4\ \text{min}$, as shown in the figure.
- a) What is his speed while walking, in $\text{m/min}$?
- b) What is his average speed for the whole journey?
- c) Why are the two results different?
Back to the beginning: Wilkin runs at $5\ \text{m/s}$, which is $18\ \text{km/h}$. Yaritza goes at $30 \div 2 = 15\ \text{km/h}$. Wilkin 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 $70\ \text{km/h}$.