Exercises: Uniform motion in a straight line

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

Which of these motions can be a MRU? Justify your answers.

1. a) A train travelling 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) A lift 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 with MRU covers $5\ \text{m}$ every second.

1. a) How many metres 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 aeroplane 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 motorway 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 a MRU?
3. c) If it continues like this, what position will it be at time $t = 10\ \text{s}$?

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

1. a) How long does a car travelling 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 $3\ \text{s}$?

Two cyclists leave at the same time, one from each village, along the straight $24\ \text{km}$ road connecting them. One travels at $15\ \text{km/h}$ and the other at $9\ \text{km/h}$, as shown in the figure.

1. a) At what speed do they approach each other?
2. b) How long does it take for them to meet?
3. c) What distance has each travelled when they meet?

Leo sets off walking along a straight path at $1.5\ \text{m/s}$. Sixty seconds later Nora sets off along the same path at $3\ \text{m/s}$, as shown in the figure (at the moment Nora sets off).

1. a) How much of a head start does Leo have at the moment Nora sets off?
2. b) How many metres does Nora gain on Leo each second?
3. c) How long does it take Nora to catch up with him?

An escalator ascends at $0.5\ \text{m/s}$, as shown in the figure.

1. a) If you walk up it at $1\ \text{m/s}$ relative to the steps, at what speed are you ascending relative to the shopping centre floor?
2. b) What if you walk down at $1\ \text{m/s}$ while the escalator is ascending? In which direction are you moving relative to the floor?
3. c) What would happen if you walked down at $0.5\ \text{m/s}$? Explain each case.

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? Reason your answer.

A family can go to the beach via two routes: by motorway, $120\ \text{km}$ 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 metres 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.

A fishing boat sails in a straight line at $10\ \text{km/h}$ for $3\ \text{h}$.

1. a) How far from the port is it?
2. b) At what speed must it return to be back in $2\ \text{h}$?
3. c) What is the average speed for the whole trip, there and back?