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Scalar quantities just have magnitude

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Energy

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Distance

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Speed

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Mass

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Vectors have magnitude and direction

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Velocity

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Displacement

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Acceleration

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Force

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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}

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Gradient gives velocity

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Area irrelevant

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Gradient gives acceleration

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Area gives total displacement

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

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The atmosphere exerts a drag force, \(d\), on any falling object, due to air resistance

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Air resistance increase with speed

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At terminal velocity, air resistance is equal to the gravitational force: \(d=mg\).

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The horizontal and vertical components are independent of each other

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Centre of mass is used as a point mass

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Components must be resolved

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.