Uniform rectilinear motion

An airport moving walkway moves in a straight line and always advances at the same speed.

1. a) What type of motion does it describe?
2. b) State the two conditions that motion must satisfy to be uniform and linear.

A luggage conveyor belt moves at $0,5\ \text{m/s}$. If the belt is $30\ \text{m}$ long, how long does it take a suitcase to travel from end to end?

A pedestrian moves with uniform linear motion according to the equation $x = x_0 + v \cdot t$, with $x_0 = 10\ \text{m}$ and $v = 2\ \text{m/s}$. Calculate their position when $t = 5\ \text{s}$.

The position of a scooter, in International System units, is $x = 50 - 4 \cdot t$.

1. a) Explain what the minus sign on the velocity means: is it moving away from or towards the origin?
2. b) Calculate its position when $t = 5\ \text{s}$.

The position of a cyclist, in International System units, is $x = 20 + 5 \cdot t$.

1. a) What is their position when $t = 6\ \text{s}$?
2. b) At what instant do they pass through position $x = 120\ \text{m}$?

A runner maintains a constant speed of $18\ \text{km/h}$.

1. a) Express their speed in $\text{m/s}$.
2. b) How long does it take them to cover $200\ \text{m}$?

A train passes through a station without stopping, at $108\ \text{km/h}$, and maintains that speed. We take the station as the origin.

1. a) Express the speed in $\text{m/s}$.
2. b) Write the equation for its position.
3. c) Calculate its position $45\ \text{s}$ after passing through the station.

Light travels in a vacuum at $3 \cdot 10^{8}\ \text{m/s}$ and the average distance from the Sun to the Earth is $1,5 \cdot 10^{11}\ \text{m}$. The diagram is shown in the figure.

1. a) Calculate the time it takes for sunlight to reach us, in seconds.
2. b) Express it in minutes, to one decimal place.

Two runners describe their motion, in International System units, using the equations $x = 8 + 2 \cdot t$ and $x = 8 + 5 \cdot t$. The $x$-$t$ graphs for both are shown in the figure.

1. a) What do the two motions have in common, and how do they differ?
2. b) Calculate the position of each runner when $t = 4\ \text{s}$.

Along a straight cycle path, two people are travelling in the same direction: A at $x_A = 5 \cdot t$ and B at $x_B = 60 + 2 \cdot t$, in International System units. The initial situation is shown in the figure.

1. a) Calculate the position of each person when $t = 8\ \text{s}$.
2. b) What distance separates them at that instant?

Two objects describe their motion, in International System units, using the equations $x_A = 3 + 5 \cdot t$ and $x_B = 10 + 5 \cdot t$. The $x$-$t$ graphs for both are shown in the figure.

1. a) Try to calculate the instant at which they would meet by equating the two equations, and explain what happens.
2. b) What distance separates them at any instant? Prove it by calculating their positions at two different instants.
3. c) State the condition that the speeds of two objects undergoing uniform linear motion must satisfy in order for them to meet.

Two cities are connected by a straight railway line of $300\ \text{km}$. A train leaves city A for B at $90\ \text{km/h}$ and, at the same time, another leaves city B for A at $60\ \text{km/h}$. The situation is shown in the figure.

1. a) How many kilometres do they get closer to each other every hour?
2. b) How long do they take to cross paths?
3. c) At what distance from city A do they cross paths?

Ana leaves her house walking at $4\ \text{m/s}$. Twenty seconds later, Bruno leaves the same house in the same direction, running at $6\ \text{m/s}$. The situation at the instant Bruno leaves is shown in the figure.

1. a) Write the position equations for both, counting time from when Bruno leaves.
2. b) Calculate the time it takes for Bruno to catch up with Ana.
3. c) At what distance from house does he catch up?
4. d) Check who is ahead $10\ \text{s}$ after Bruno leaves and explain the result.

Two athletes train on a straight track with equations, in International System units, $x_A = 2 + 4 \cdot t$ and $x_B = 10 + 2 \cdot t$.

1. a) Which of the two starts further ahead, and with how many metres head start?
2. b) Calculate the instant and position where one catches up with the other.
3. c) Determine the position of each athlete when $t = 10\ \text{s}$ and the distance between them.
4. d) Explain, based on their speeds, why the one who started behind ends up taking the lead.