| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2018 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Forces in vector form: kinematics extension |
| Difficulty | Moderate -0.3 This is a straightforward M1 mechanics question requiring vector addition of forces, application of F=ma, and basic kinematics with constant acceleration. All steps are routine: add forces, divide by mass for acceleration, find magnitude, then use v=u+at in component form. Slightly easier than average due to being purely procedural with no problem-solving insight required. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10c Magnitude and direction: of vectors3.03d Newton's second law: 2D vectors |
\begin{enumerate}
\item \hspace{0pt} [In this question $\mathbf { i }$ and $\mathbf { j }$ are perpendicular horizontal unit vectors.]
\end{enumerate}
A particle $P$ of mass 2 kg moves under the action of two forces, $( 2 \mathbf { i } + 3 \mathbf { j } ) \mathrm { N }$ and $( 4 \mathbf { i } - 5 \mathbf { j } ) \mathrm { N }$.\\
(a) Find the magnitude of the acceleration of $P$.
At time $t = 0 , P$ has velocity ( $- u \mathbf { i } + u \mathbf { j }$ ) $\mathrm { m } \mathrm { s } ^ { - 1 }$, where $u$ is a positive constant.
At time $t = T$ seconds, $P$ has velocity $( 10 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$.\\
(b) Find\\
(i) the value of $T$,\\
(ii) the value of $u$.\\
\hfill \mbox{\textit{Edexcel M1 2018 Q6 [9]}}