Position, trajectory and displacement

You want to explain over the phone to a friend where your backpack is in the classroom. What point in the classroom would you choose as a reference to describe its position? Explain in your own words what a frame of reference is.

Along a straight line measured in metres, Pablo is at position $x = 3\ \text{m}$, taking a tree as the origin, as shown in the figure.

What does this data mean? Where would Pablo be if his position were $x = -3\ \text{m}$?

Leo says: "I am $10\ \text{m}$ away." His sister asks him: "$10\ \text{m}$ away from where?"

1. a) Explain what information is missing from Leo's sentence and why a position always requires a frame of reference.
2. b) Leo is $10\ \text{m}$ from a lamppost, and the lamppost is $6\ \text{m}$ from the bus stop, all on the same straight street. How far from the bus stop could Leo be? Give both possibilities.

An ant walks along the edge of a square table until it returns to the starting point. Is its path straight or curved? Explain what the path of a motion is.

A kitchen robot moves forward $3\ \text{m}$ in a straight line, turns at a right angle, and moves forward another $4\ \text{m}$, as shown in the figure.

What total distance has it covered?

Lucía walks along a straight corridor: she moves forward $4\ \text{m}$ to the right and then moves back $3\ \text{m}$ to the left, as shown in the figure.

1. a) What total distance has she covered?
2. b) What was her displacement?

Sara leaves the front door of her house (the origin), walks $60\ \text{m}$ in a straight line towards the park, and then turns back $25\ \text{m}$ towards home, as shown in the figure.

1. a) What distance has she covered?
2. b) What is her final position?
3. c) What was her displacement?

A robot vacuum cleaner moves along a straight corridor: it moves forward $5\ \text{m}$, moves back $3\ \text{m}$, and finally moves forward $2\ \text{m}$, as shown in the figure.

1. a) What total distance has it covered?
2. b) What was its displacement?
3. c) Do both values coincide? Explain in what type of motion distance and displacement are equal.

A drone flies $30\ \text{m}$ north and then $40\ \text{m}$ east, as shown in the figure.

1. a) What distance has it covered?
2. b) Calculate its displacement. Hint: the displacement is the hypotenuse of a right-angled triangle; use Pythagoras' theorem.

A postman walks around a block: he walks $60\ \text{m}$ along one street, turns at a right angle, and walks $80\ \text{m}$ along the next street.

1. a) What distance has he covered?
2. b) If he could return to the starting point in a straight line, how far would he walk? Use Pythagoras' theorem.

A rectangular pitch measures $30\ \text{m}$ wide by $40\ \text{m}$ long. One player goes from one corner to the opposite corner along the edge of the pitch, and another crosses along the diagonal, as shown in the figure.

1. a) What distance does each person cover?
2. b) What is the displacement of each person?
3. c) What conclusion do you draw about distance and displacement?