Exercises: Speed

A runner covers $100\ \text{m}$ in $20\ \text{s}$. Calculate their average speed in $\text{m/s}$.

A cyclist covers $30\ \text{km}$ in $2\ \text{h}$. What is their average speed in $\text{km/h}$?

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...".

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.

State which of these expressions are units of speed and which are not, and explain why:

1. a) $\text{m/s}$
2. b) $\text{km}$
3. c) $\text{km/h}$
4. d) $\text{s}$

A snail covers $2\ \text{m}$ in $10\ \text{min}$. What is its speed in $\text{m/min}$?

I walk at a constant speed of $2\ \text{m/s}$. How long does it take me to cover $10\ \text{m}$?

Complete the sentence with the missing words: "Average speed is calculated by dividing the $\dots$ covered by the $\dots$ taken." Then provide an example with numbers.

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 toy train travels $300\ \text{m}$ in $1\ \text{min}$. What is its speed in $\text{m/s}$?

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.

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 falcon glides at $8\ \text{m/s}$ for $30\ \text{s}$. What distance does it cover in that time?

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.

1. a) What is the total distance covered and how much time did it take?
2. b) What is her average speed for the whole journey?
3. c) What was her total displacement? Explain the difference between displacement and distance.

Order the following speeds from lowest to highest, expressing them all in $\text{m/s}$ first:

1. a) $18\ \text{km/h}$
2. b) $10\ \text{m/s}$
3. c) $900\ \text{m/min}$

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.

1. a) Calculate the time taken for each section.
2. b) Calculate the average speed for the whole trip.
3. c) Explain why the average speed is not $90\ \text{km/h}$, the mean of the two speeds.

You shout in front of a mountain and hear the echo $2\ \text{s}$ later. Sound travels through the air at $340\ \text{m/s}$, as shown in the figure.

1. a) What distance has the sound travelled in those $2\ \text{s}$?
2. b) How far away from you is the mountain?
3. c) Explain why you need to divide by $2$ in the previous part.

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.

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.

1. a) What is his speed while walking, in $\text{m/min}$?
2. b) What is his average speed for the whole journey?
3. c) Why are the two results different?

Mei walks to her training, which is $2\ \text{km}$ from home, at a speed of $4\ \text{km/h}$. Bea cycles to the sports centre, which is $9\ \text{km}$ away, at $12\ \text{km/h}$. They both leave at the same time.

1. a) How long does each of them take?
2. b) Express both times in minutes.
3. c) Who arrives first?

A train needs to travel the last $500\ \text{m}$ before the station and has $30\ \text{s}$ to arrive on time. It travels at $20\ \text{m/s}$.

1. a) How long does it take to travel those $500\ \text{m}$?
2. b) Will it arrive on time?
3. c) By how many seconds does it arrive early or late?

In a relay race of $4$ legs of $100\ \text{m}$ each, a team sets these times: $12\ \text{s}$, $13\ \text{s}$, $11\ \text{s}$ and $14\ \text{s}$.

1. a) What is the team's total time?
2. b) What is the team's average speed over the $400\ \text{m}$?
3. c) If they wanted an average speed of $10\ \text{m/s}$, in what time would they have to run the $400\ \text{m}$?

A cyclist covers $3\ \text{km}$ in $10\ \text{min}$ with a tailwind and takes $15\ \text{min}$ to return along the same route.

1. a) Calculate her speed on the outward and return journeys, in $\text{km/h}$.
2. b) Calculate her average speed for the complete trip.
3. c) Is the average speed equal to the mean of the two speeds from part a)? Reason your answer.