0.2 Motion in one dimension  (Page 2/16)

For this chapter, we will only use frames of reference in the $x$ -direction. Frames of reference will be covered in more detail in Grade 12.

Position

Position

Position is a measurement of a location, with reference to an origin.

A position is a measurement of a location, with reference to an origin. Positions can therefore be negative or positive. The symbol $x$ is used to indicate position. $x$ has units of length for example cm, m or km. [link] shows the position of a school. Depending on what reference point we choose, we can say that the school is $300\mathrm{m}$ from Joan's house (with Joan's house as the reference point or origin) or $500\mathrm{m}$ from Joel's house (with Joel's house as the reference point or origin).

The shop is also $300m$ from Joan's house, but in the opposite direction as the school. When we choose a reference point, we have a positive direction and a negative direction. If we choose the direction towards the school as positive, then the direction towards the shop is negative. A negative direction is always opposite to the direction chosen as positive.

Discussion : reference points

Divide into groups of 5 for this activity. On a straight line, choose a reference point. Since position can have both positive and negative values, discuss the advantages and disadvantages of choosing

1. either end of the line,
2. the middle of the line.

This reference point can also be called “the origin".

Position

1. Write down the positions for objects at A, B, D and E. Do not forget the units.

   

2. Write down the positions for objects at F, G, H and J. Do not forget the units.

   

3. There are 5 houses on Newton Street, A, B, C, D and E. For all cases, assume that positions to the right are positive.

   

   1. Draw a frame of reference with house A as the origin and write down the positions of houses B, C, D and E.
   2. You live in house C. What is your position relative to house E?
   3. What are the positions of houses A, B and D, if house B is taken as the reference point?

Displacement and distance

Displacement

Displacement is the change in an object's position.

The displacement of an object is defined as its change in position (final position minus initial position). Displacement has a magnitude and direction and is therefore a vector. For example, if the initial position of a car is $x_i$ and it moves to a final position of $x_f$ , then the displacement is:

However, subtracting an initial quantity from a final quantity happens often in Physics, so we use the shortcut $\Delta$ to mean final - initial . Therefore, displacement can be written: