| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2017 |
| 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 -0.8 This is a straightforward M1 mechanics question requiring basic application of F=ma in vector form, constant acceleration kinematics (v = u + at), and understanding of parallel vectors. All three parts use standard techniques with no problem-solving insight needed, making it easier than average but not trivial due to the vector notation requirement. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10d Vector operations: addition and scalar multiplication3.03d Newton's second law: 2D vectors |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Use of \(\mathbf{F} = m\mathbf{a}\): \(2\mathbf{i} + 3\mathbf{j} = 0.5\mathbf{a}\) | M1 | M1 for use of \(\mathbf{F} = m\mathbf{a}\) |
| \(\mathbf{a} = 4\mathbf{i} + 6\mathbf{j}\) (m s\(^{-2}\)) | A1 | A1 for \(4\mathbf{i} + 6\mathbf{j}\) (m s\(^{-2}\)) isw if magnitude found |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Use of \(\mathbf{v} = \mathbf{u} + 3\mathbf{a}\) with their \(\mathbf{a}\) | M1 | First M1 for \(\mathbf{v} = 4\mathbf{i} + 3(4\mathbf{i} + 6\mathbf{j})\) with their \(\mathbf{a}\) (but M0 if they use \(2\mathbf{i} + 3\mathbf{j}\) instead of \(\mathbf{a}\)) |
| \(= 16\mathbf{i} + 18\mathbf{j}\) | A1 | First A1 for \(16\mathbf{i} + 18\mathbf{j}\) seen or implied |
| Use of Pythagoras: speed \(= \sqrt{16^2 + 18^2}\) | M1 | Second M1 for finding magnitude of their \(\mathbf{v}\) |
| \(= \sqrt{580}\) or 24 (m s\(^{-1}\)) or better | A1 | Second A1 for 24 or better (24.0831...) or \(\sqrt{580}\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| In component form: \(\mathbf{v} = 4\mathbf{i} + t(4\mathbf{i} + 6\mathbf{j})\) | M1 | First M1 for \(\mathbf{v} = 4\mathbf{i} + t(4\mathbf{i} + 6\mathbf{j})\) with their \(\mathbf{a}\) (but M0 if they use \(2\mathbf{i} + 3\mathbf{j}\) instead of \(\mathbf{a}\)) |
| \(4 + 4T = 2 \times 6T\) | M1 | Second independent M1 for a correct method to give an equation in \(T\) (t) only using their \(\mathbf{v}\) |
| \(T = \dfrac{1}{2}\) | A1 | A1 for \((T) = \frac{1}{2}\) |
# Question 2:
## Part 2a:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Use of $\mathbf{F} = m\mathbf{a}$: $2\mathbf{i} + 3\mathbf{j} = 0.5\mathbf{a}$ | M1 | M1 for use of $\mathbf{F} = m\mathbf{a}$ |
| $\mathbf{a} = 4\mathbf{i} + 6\mathbf{j}$ (m s$^{-2}$) | A1 | A1 for $4\mathbf{i} + 6\mathbf{j}$ (m s$^{-2}$) isw if magnitude found |
## Part 2b:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Use of $\mathbf{v} = \mathbf{u} + 3\mathbf{a}$ with their $\mathbf{a}$ | M1 | First M1 for $\mathbf{v} = 4\mathbf{i} + 3(4\mathbf{i} + 6\mathbf{j})$ with their $\mathbf{a}$ (but M0 if they use $2\mathbf{i} + 3\mathbf{j}$ instead of $\mathbf{a}$) |
| $= 16\mathbf{i} + 18\mathbf{j}$ | A1 | First A1 for $16\mathbf{i} + 18\mathbf{j}$ seen or implied |
| Use of Pythagoras: speed $= \sqrt{16^2 + 18^2}$ | M1 | Second M1 for finding magnitude of their $\mathbf{v}$ |
| $= \sqrt{580}$ or 24 (m s$^{-1}$) or better | A1 | Second A1 for 24 or better (24.0831...) or $\sqrt{580}$ |
## Part 2c:
| Answer/Working | Mark | Guidance |
|---|---|---|
| In component form: $\mathbf{v} = 4\mathbf{i} + t(4\mathbf{i} + 6\mathbf{j})$ | M1 | First M1 for $\mathbf{v} = 4\mathbf{i} + t(4\mathbf{i} + 6\mathbf{j})$ with their $\mathbf{a}$ (but M0 if they use $2\mathbf{i} + 3\mathbf{j}$ instead of $\mathbf{a}$) |
| $4 + 4T = 2 \times 6T$ | M1 | Second independent M1 for a correct method to give an equation in $T$ (t) only using their $\mathbf{v}$ |
| $T = \dfrac{1}{2}$ | A1 | A1 for $(T) = \frac{1}{2}$ |
---\begin{enumerate}
\item A particle $P$ of mass 0.5 kg moves under the action of a single constant force ( $2 \mathbf { i } + 3 \mathbf { j }$ )N.\\
(a) Find the acceleration of $P$.
\end{enumerate}
At time $t$ seconds, $P$ has velocity $\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }$. When $t = 0 , \mathbf { v } = 4 \mathbf { i }$\\
(b) Find the speed of $P$ when $t = 3$
Given that $P$ is moving parallel to the vector $2 \mathbf { i } + \mathbf { j }$ at time $t = T$\\
(c) find the value of $T$.\\
\hfill \mbox{\textit{Edexcel M1 2017 Q2 [9]}}