Exercises: Uniform motion in a straight line

Explain in your own words what uniform motion in a straight line is: what is its trajectory like? What is its speed like?

Which of these motions can be uniform rectilinear motion (constant velocity in a straight line)? Justify your answers.

1. a) A train traveling along a straight track at $120\ \text{km/h}$ without changing its speed.
2. b) A car stuck in a traffic jam.
3. c) A luggage conveyor belt that turns on curves.
4. d) An elevator ascending at a constant speed.

An electric scooter travels $60\ \text{m}$ in $12\ \text{s}$ along a straight street, without changing its speed. What is its speed?

The conveyor belt at a supermarket checkout moves the groceries $2\ \text{m}$ in $10\ \text{s}$. At what speed is the belt moving?

An object moving at constant velocity (uniform rectilinear motion) covers $5\ \text{m}$ every second.

1. a) How many meters does it cover in $4\ \text{s}$?
2. b) And in $10\ \text{s}$?

Complete the sentence with the missing words: "In uniform motion in a straight line, the trajectory is a $\dots$ line and the speed is $\dots$". Then give a real-life example.

An airplane flies in a straight line and covers $150\ \text{km}$ in $0.5\ \text{h}$ at constant speed. What is its speed in $\text{km/h}$?

A tortoise moves in a straight line at $0.3\ \text{m/s}$ for $10\ \text{s}$. What distance does it cover?

How long does it take a car to cover $240\ \text{km}$ on a highway if it maintains a constant speed of $80\ \text{km/h}$?

A cyclist goes down a mountain pass at $72\ \text{km/h}$.

1. a) Express their speed in $\text{m/s}$.
2. b) What distance do they cover in $15\ \text{s}$ at that speed?

A runner maintains a constant speed of $5\ \text{m/s}$. How long does it take them to cover $900\ \text{m}$? Give the answer in seconds and in minutes.

A construction hoist rises at $0.5\ \text{m/s}$. How long does it take to get from the ground to scaffolding $12\ \text{m}$ high?

An object passes through the positions $x = 0\ \text{m}$, $4\ \text{m}$, $8\ \text{m}$ and $12\ \text{m}$ at times $t = 0\ \text{s}$, $1\ \text{s}$, $2\ \text{s}$ and $3\ \text{s}$, as shown in the figure.

1. a) What distance does it cover each second?
2. b) What is its speed? Is it uniform rectilinear motion (constant velocity)?
3. c) If it continues like this, what position will it be at time $t = 10\ \text{s}$?

Between two towns there are $30\ \text{km}$ of straight road.

1. a) How long does a car traveling at $60\ \text{km/h}$ take? Give the answer in hours and in minutes.
2. b) At what speed would it have to travel to take only $20\ \text{min}$?

A boat sails in a straight line at $18\ \text{km/h}$ for $30\ \text{min}$. What distance does it cover?

Measuring every second, a car travels $10\ \text{m}$ in the first second, $15\ \text{m}$ in the second second and $20\ \text{m}$ in the third second.

1. a) Is it uniform motion in a straight line? Why?
2. b) What is its average speed during those $3\ \text{s}$?

Sunlight travels $1.5\times10^{8}\ \text{km}$ to Earth at a speed of $3\times10^{5}\ \text{km/s}$.

1. a) How many seconds does it take for sunlight to reach us?
2. b) Express the answer in minutes and seconds.
3. c) If the Sun were to suddenly go out, when would we see it from Earth? Explain your reasoning.

A family can go to the beach via two routes: by highway, $120\ \text{km}$ at $100\ \text{km/h}$, or by main road, $90\ \text{km}$ at $60\ \text{km/h}$.

1. a) Calculate the time they take for each route, in hours.
2. b) Express those times in minutes.
3. c) Which route gets them there faster? How many minutes difference is there?

A bus departs at 10:00 and needs to travel $45\ \text{km}$ at a constant speed of $60\ \text{km/h}$.

1. a) What time does it arrive at its destination?
2. b) If a traffic jam forces it to travel at $45\ \text{km/h}$, what time would it arrive?
3. c) How many minutes late is it in that case?

At the gym, the treadmill displays $12\ \text{km/h}$.

1. a) How many meters does a runner "cover" in $5\ \text{min}$ on the treadmill?
2. b) Has she changed position relative to the gym floor? Explain the difference between motion relative to the treadmill and relative to the floor.