| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (vectors) |
| Type | Constant acceleration vector problems |
| Difficulty | Moderate -0.5 This is a straightforward M1 mechanics question requiring standard application of Newton's second law with vectors. Part (a) is simple magnitude calculation, part (b) uses F=ma with constant acceleration found from velocity change, and part (c) requires setting the j-component of velocity to zero. All steps are routine with no problem-solving insight needed, making it slightly easier than average. |
| Spec | 1.10c Magnitude and direction: of vectors3.02b Kinematic graphs: displacement-time and velocity-time3.03d Newton's second law: 2D vectors |
| Answer | Marks | Guidance |
|---|---|---|
| Part | Answer/Working | Marks |
| (a) | speed \(= \sqrt{2^2 + (-5)^2} = \sqrt{29} = 5.4\) or better | M1 A1 |
| (b) | \(((7i + 10j) - (2i - 5j))/5 = (5i + 15j)/5 = i + 3j\) | M1 A1 A1 |
| \(F = ma = 2(i + 3j) = 2i + 6j\) | DM1 A1 ft | (5 marks) |
| (c) | \(v = u + at = (2i - 5j) + (i + 3j)t = (-5 + 3t)j\) | M1 A1 |
| Parallel to \(i \Rightarrow -5 + 3t = 0\) → \(t = 5/3\) | M1 A1 | (4 marks) |
| [11 marks total] |
| **Part** | **Answer/Working** | **Marks** | **Guidance** |
|----------|-------------------|----------|-------------|
| (a) | speed $= \sqrt{2^2 + (-5)^2} = \sqrt{29} = 5.4$ or better | M1 A1 | (2 marks) |
| (b) | $((7i + 10j) - (2i - 5j))/5 = (5i + 15j)/5 = i + 3j$ | M1 A1 A1 | |
| | $F = ma = 2(i + 3j) = 2i + 6j$ | DM1 A1 ft | (5 marks) |
| (c) | $v = u + at = (2i - 5j) + (i + 3j)t = (-5 + 3t)j$ | M1 A1 | |
| | Parallel to $i \Rightarrow -5 + 3t = 0$ → $t = 5/3$ | M1 A1 | (4 marks) |
| | | | **[11 marks total]** |\begin{enumerate}
\item A particle $P$ of mass 2 kg is moving under the action of a constant force $\mathbf { F }$ newtons. The velocity of $P$ is $( 2 \mathbf { i } - 5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ at time $t = 0$, and $( 7 \mathbf { i } + 10 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ at time $t = 5 \mathrm {~s}$.
\end{enumerate}
Find\\
(a) the speed of $P$ at $t = 0$,\\
(b) the vector $\mathbf { F }$ in the form $a \mathbf { i } + b \mathbf { j }$,\\
(c) the value of $t$ when $P$ is moving parallel to $\mathbf { i }$.\\
\hfill \mbox{\textit{Edexcel M1 2011 Q4 [11]}}