OCR MEI M1 2008 January — Question 2 7 marks

Exam BoardOCR MEI
ModuleM1 (Mechanics 1)
Year2008
SessionJanuary
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicForces, equilibrium and resultants
TypeForces in vector form: kinematics extension
DifficultyModerate -0.8 This is a straightforward M1 mechanics question requiring direct application of F=ma to find acceleration vector, basic trigonometry (arctan) for angle, and constant acceleration kinematics (s=ut+½at²) with vectors. All three parts are routine calculations with no problem-solving insight needed, making it easier than average but not trivial due to the vector manipulation and multi-step nature.
Spec1.10d Vector operations: addition and scalar multiplication3.02e Two-dimensional constant acceleration: with vectors3.03d Newton's second law: 2D vectors

The force acting on a particle of mass 1.5 kg is given by the vector \(\begin{pmatrix} 6 \\ 9 \end{pmatrix}\) N.
  1. Give the acceleration of the particle as a vector. [2]
  2. Calculate the angle that the acceleration makes with the direction \(\begin{pmatrix} 1 \\ 0 \end{pmatrix}\). [2]
  3. At a certain point of its motion, the particle has a velocity of \(\begin{pmatrix} -2 \\ 3 \end{pmatrix}\) m s\(^{-1}\). Calculate the displacement of the particle over the next two seconds. [3]

The force acting on a particle of mass 1.5 kg is given by the vector $\begin{pmatrix} 6 \\ 9 \end{pmatrix}$ N.

\begin{enumerate}[label=(\roman*)]
\item Give the acceleration of the particle as a vector. [2]
\item Calculate the angle that the acceleration makes with the direction $\begin{pmatrix} 1 \\ 0 \end{pmatrix}$. [2]
\item At a certain point of its motion, the particle has a velocity of $\begin{pmatrix} -2 \\ 3 \end{pmatrix}$ m s$^{-1}$. Calculate the displacement of the particle over the next two seconds. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI M1 2008 Q2 [7]}}