# Physics, Motion and Forces, 9-12

## Equations of Motion

### Scalars and Vectors

• Scalar quantities just have magnitude

• Energy

• Distance

• Speed

• Mass

• Vectors have magnitude and direction

• Velocity

• Displacement

• Acceleration

• Force

## Relative Velocity

Velocity is relative and must be taken with respect to a frame of reference, although this is typically the surface of the Earth.

Vectors can be drawn to scale, and must form a closed shape to show the resultant vector. A vector can also be resolved into horizontal and vertical components which can then be considered independently of each other.

## Acceleration

$$a=\frac{\Delta v}{\Delta t}\nonumber \\$$

## Time and Motion Graphs

### Displacement-Time Graphs

• Area irrelevant

### Velocity-Time Graphs

• Area gives total displacement

## Equations of Motion

These can only be used with constant acceleration.

\begin{gather} v=u+at \\ s=ut+\frac{1}{2}at^{2} \\ s=vt-\frac{1}{2}at^{2} \\ v^{2}=u^{2}+2as \\ s=\frac{u+v}{2}t\\ \end{gather}

## Free Fall and Terminal Velocity

An object is in free fall if the only force acting on it is the gravitational force.

### The Effect of Air Resistance

• The atmosphere exerts a drag force, $$d$$, on any falling object, due to air resistance

• Air resistance increase with speed

\begin{align} & d\propto v\notag \\ & d\propto v^{2}\notag \\ \end{align}
• At terminal velocity, air resistance is equal to the gravitational force: $$d=mg$$.

## Projectile Motion in Two Dimensions

• The horizontal and vertical components are independent of each other

• Centre of mass is used as a point mass

• Components must be resolved

## Forces in Balance

### Statics

Statics is the branch of mechanics that deals with forces which are in equilibrium.

#### Weight

$$w=mg\\$$

Weight is the force that acts on a mass due to a gravitational attraction, and acts through the centre of gravity. The centre of mass is different - a force applied through the centre of mass would cause no rotation.

• The