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.


\begin{equation} a=\frac{\Delta v}{\Delta t}\nonumber \\ \end{equation}

Time and Motion Graphs

Displacement-Time Graphs

  • Gradient gives velocity

  • Area irrelevant

Velocity-Time Graphs

  • Gradient gives acceleration

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


\begin{equation} w=mg\\ \end{equation}

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.

Contact Force

  • The