## Motion

- Motion is a fundamental observable phenomenon.
- The study of Kinematics involves describing, measuring, and analysing motion without considering the forces and masses involved.

## Scalars and Vectors

- Scalars are physical quantities that can be described as a magnitude, with a unit (for example, 60km/h)
- Examples of Scalars include time, distance, volume, and speed
- Scalars are represented by a simple italic symbol, such as
*t*for time or*d*for distance

- Vectors are physical quantities that can be described as a magnitude, a unit and a direction (for example, 20m West)
- Examples of Vectors include position, displacement, velocity, acceleration, and force
- Vectors are represented using VECTOR NOTATION.
- The most common type of vector notation uses an arrow above the symbol, for example $\vec{v}$ for Velocity

## Adding and Subtracting Vectors Using Algebra (One Dimension)

- When adding or subtracting vectors using algebra, a sign convention must be established to represent the direction
- For example, positive for forwards and negative for backwards
- When using a sign convention it is CRUCIAL to provide a key explaining the convention used.
- Using a sign convention allows you to enter the directions and magnitudes into your calculator. The sign of the final magnitude gives the direction of the total vector.

### Steps for Adding

- Apply the sign convention to change each of the directions to signs
- Add their magnitudes and their signs together
- Refer to the sign convention to determine to direction of thr resultant vector
- State the resultant vector

- Example:
- A student walks 25m forward, then 16m backward, then 44m forward, then 12m backward. Determine the total displacement.

- Forward is positive

- 25m forward = 25m
- 16m backward = -16m
- 44m forward = 44m
- 12m backward = -12m

- $25-16+44-12 = +41$
- Positive is forward
- Therefore, the total displacement is 41m forward.

### Steps for Subtracting

- Apply the sign convention to change each of the directions to signs
- Reverse the direction of the initial vector by reversing the sign
- Do vector addition with the results

- Example:
- An aeroplane changes course from 255m/s West to 160m/s East. Determine the change in velocity.

- West is negative

- 225m/s West = -255m/s $\vec{v}_1$
- 160m/s East = 160m/s $\vec{v}_2$

- Reverse the initial vector: $-\vec{v}_1$ = 255m/s
- Add the vectors: $-\vec{v}_1 + \vec{v}_2 = 225+160 = 415m/s$
- Positive is east, therefore the change in velocity is 415m/s East

## Displacement, Speed and Velocity

- This section will explain the terms and concepts of RECTILINEAR (straight-line), such as position, distance, displacement, speed and velocity.

### Center of Mass

- An object’s motion is described in terms of their CENTER OF MASS, a single point which is the balance point of the object.

### Position

- Position describes the location of an object at a certain point in time with respect to the origin.
- Position is a vector quantity and therefore requires a direction. The absolute reference frame for the direction is the origin of the object.
- Position is measured in metres.

### Distance Travelled

- Distance Travelled describes how far a body travels during a journey.
- Distance is a scalar quantity and is measured in meters.

### Displacement

- Displacement is the change in position of an object, and is represented by the symbol $\vec{s}$
- Displacement considers only the starting point and ending point
- In other words, the displacement of an object is the straight-line distance between its start and end points

- Displacement is calculated by subtracting the initial position from the final position
- Displacement is a VECTOR and therefore must have a direction as well as a magnitude

#### Displacement-Time Graphs

- Displacement-time graphs can be used to summarise the motion of an object
- The gradient of the graph at any point is the velocity at that point

## Speed and Velocity

- Speed is the rate at which distance is travelled
- Speed is SCALAR

- Velocity is the rate at which displacement changes
- Velocity is a VECTOR

- Speed and velocity are both measured in $m/s^2$

### Instantaneous Speed and Velocity

- How fast an object is moving at a particular point in time
- The instantaneous speed is ALWAYS equal to the magnitude of the instantaneous velocity

### Average Speed and Velocity

- Indication of how fast an object is moving over a period of time
- Average Speed: $v_{av} = \frac{\text{Distance Travelled}}{\text{Time Taken}} = \frac{d}{\Delta t}$
- Average Velocity: $\vec{v_{av}} = \frac{\text{Displacement}}{\text{Time Taken}} = \frac{\vec{d}}{\Delta t}$

## Converting between km/h and m/s

- To convert km/h to m/s, divide by 3.6
- To convert from m/s to km/h, multiply by 3.6

## SUVAT Equations

- These can also be expressed with different subjects: