Uniform rectilinear motion

Explain what the acronym MRU stands for and describe two real-life examples of motion that, at least for a while, can be considered MRU.

A walker starts from position $x_0 = 10\ \text{m}$ and moves forward in a straight line at $2\ \text{m/s}$, as shown in the figure.

Using the equation $x = x_0 + v\cdot t$, calculate her position after $5\ \text{s}$.

A runner starts from the origin ($x_0 = 0\ \text{m}$) and runs at a constant speed of $4\ \text{m/s}$. What position are they at after $10\ \text{s}$?

The position of a train is given by the equation $x = 20 + 5\cdot t$, in SI units. From what position does it start? At what velocity is it moving? Where will it be at time $t = 10\ \text{s}$?

A toy cart undergoing MRU passes position $5\ \text{m}$ at time $t = 0\ \text{s}$ and position $45\ \text{m}$ at $t = 10\ \text{s}$. What is its velocity?

A cyclist starts from kilometre marker $12$ on a greenway and pedals to kilometre marker $32$, as shown in the figure.

What is their final position? What distance have they covered? Explain the difference between the two concepts.

A drone is at position $x_0 = 100\ \text{m}$ and flies towards the origin at $4\ \text{m/s}$, so that its velocity is negative: $v = -4\ \text{m/s}$, as shown in the figure.

1. a) Write down its position equation.
2. b) What position is it at at time $t = 10\ \text{s}$?
3. c) At what time does it pass through the origin?

A cyclist leaves the origin at $8\ \text{m/s}$. At the same time, his friend starts $30\ \text{m}$ ahead, in the same direction, at $5\ \text{m/s}$, as shown in the figure.

1. a) Write down the position equation for each person.
2. b) How long does it take the cyclist to catch up with his friend?

Two ships set sail at the same time from two ports $120\ \text{km}$ apart, sailing towards each other at $25\ \text{km/h}$ and $15\ \text{km/h}$.

1. a) How many kilometres closer to each other do they get every hour?
2. b) How long does it take for them to meet?
3. c) At what distance from the first port do they meet?

Two trains depart at the same time from two stations separated by $240\ \text{km}$, one from each station and travelling towards each other, at $100\ \text{km/h}$ and $60\ \text{km/h}$, as shown in the figure.

1. a) Write down the position equation for each train taking the first station as the origin.
2. b) Calculate at what time and at what position they cross paths.
3. c) Check the result by substituting the time into both equations.

In a charity race, Aitana runs at $4\ \text{m/s}$ and has a $60\ \text{m}$ head start over Bruno, who runs at $6\ \text{m/s}$. The finish line is $200\ \text{m}$ ahead of Aitana, as shown in the figure.

1. a) Write down the position equation for each runner, taking Bruno's position as the origin.
2. b) Calculate at what time and at what position Bruno catches up with Aitana.
3. c) Does he manage to catch up with her before the finish line? Justify your answer using calculations.