Edexcel AEA 2022 June — Question 2 10 marks

Exam BoardEdexcel
ModuleAEA (Advanced Extension Award)
Year2022
SessionJune
Marks10
PaperDownload PDF ↗
TopicVectors Introduction & 2D
TypeNewton's second law with vector forces (find acceleration or force)
DifficultyChallenging +1.2 This question requires expressing hexagon vertices in terms of two vectors, summing forces with scalar multiples, then applying F=ma. While it involves multiple steps and vector geometry, the hexagon properties are standard (120° angles), the vector addition is systematic, and the final calculation is straightforward. It's above average due to the geometric setup and multi-part nature, but doesn't require novel insight—just careful application of known techniques.
Spec1.10a Vectors in 2D: i,j notation and column vectors1.10d Vector operations: addition and scalar multiplication3.03a Force: vector nature and diagrams

2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{71cd126f-1c7d-4e37-a26d-7ff98a74fd79-04_456_508_255_781} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a regular hexagon \(O P Q R S T\).
The vectors \(\mathbf { p }\) and \(\mathbf { q }\) are defined by \(\mathbf { p } = \overrightarrow { O P }\) and \(\mathbf { q } = \overrightarrow { O Q }\) Forces, in Newtons, \(\mathbf { F } _ { P } = ( \overrightarrow { O P } ) , \mathbf { F } _ { Q } = 2 \times ( \overrightarrow { O Q } ) , \mathbf { F } _ { R } = 3 \times ( \overrightarrow { O R } ) , \mathbf { F } _ { S } = 4 \times ( \overrightarrow { O S } )\) and \(\mathbf { F } _ { T } = 5 \times ( \overrightarrow { O T } )\) are applied to a particle.
  1. Find, in terms of \(\mathbf { p }\) and \(\mathbf { q }\), the resultant force on the particle. The magnitude of the acceleration of the particle due to these forces is \(13 \mathrm {~ms} ^ { - 2 }\) Given that the mass of the particle is 3 kg ,
  2. find \(| \mathbf { p } |\) \includegraphics[max width=\textwidth, alt={}, center]{71cd126f-1c7d-4e37-a26d-7ff98a74fd79-04_2255_56_310_1980}

2.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{71cd126f-1c7d-4e37-a26d-7ff98a74fd79-04_456_508_255_781}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}

Figure 1 shows a regular hexagon $O P Q R S T$.\\
The vectors $\mathbf { p }$ and $\mathbf { q }$ are defined by $\mathbf { p } = \overrightarrow { O P }$ and $\mathbf { q } = \overrightarrow { O Q }$\\
Forces, in Newtons, $\mathbf { F } _ { P } = ( \overrightarrow { O P } ) , \mathbf { F } _ { Q } = 2 \times ( \overrightarrow { O Q } ) , \mathbf { F } _ { R } = 3 \times ( \overrightarrow { O R } ) , \mathbf { F } _ { S } = 4 \times ( \overrightarrow { O S } )$ and $\mathbf { F } _ { T } = 5 \times ( \overrightarrow { O T } )$ are applied to a particle.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $\mathbf { p }$ and $\mathbf { q }$, the resultant force on the particle.

The magnitude of the acceleration of the particle due to these forces is $13 \mathrm {~ms} ^ { - 2 }$\\
Given that the mass of the particle is 3 kg ,
\item find $| \mathbf { p } |$\\
\includegraphics[max width=\textwidth, alt={}, center]{71cd126f-1c7d-4e37-a26d-7ff98a74fd79-04_2255_56_310_1980}
\end{enumerate}

\hfill \mbox{\textit{Edexcel AEA 2022 Q2 [10]}}