| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Constant acceleration vector (i and j) |
| Difficulty | Moderate -0.3 This is a straightforward M1 vector kinematics problem requiring application of v = u + at in component form and the magnitude formula. Students set up two equations from the i and j components, use the magnitude condition to get a third equation, then solve the system. While it involves vectors and simultaneous equations, it's a standard textbook exercise with no novel insight required—slightly easier than average due to its routine nature. |
| Spec | 1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication3.02e Two-dimensional constant acceleration: with vectors |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \((2\mathbf{i}+9\mathbf{j})-(-3\mathbf{i}-3\mathbf{j})\) | M1 | Use of \(\mathbf{v}-\mathbf{u}(=\mathbf{a}t)\) seen or implied |
| \(=(5\mathbf{i}+12\mathbf{j})\) | A1 | |
| \(k^2(5^2+12^2)=2.6^2 \quad (k=1/t)\) | M1 | Use magnitude \(=2.6=k |
| \(c=5\times0.2=1\) | A1 | |
| \(d=12\times0.2=2.4\) | A1 | |
| (5) |
## Question 7:
| Working | Mark | Guidance |
|---------|------|----------|
| $(2\mathbf{i}+9\mathbf{j})-(-3\mathbf{i}-3\mathbf{j})$ | M1 | Use of $\mathbf{v}-\mathbf{u}(=\mathbf{a}t)$ seen or implied |
| $=(5\mathbf{i}+12\mathbf{j})$ | A1 | |
| $k^2(5^2+12^2)=2.6^2 \quad (k=1/t)$ | M1 | Use magnitude $=2.6=k|\mathbf{a}|$ (linking 2.6 & 13) |
| $c=5\times0.2=1$ | A1 | |
| $d=12\times0.2=2.4$ | A1 | |
| | **(5)** | |
---\begin{enumerate}
\item A particle $P$ moves from point $A$ to point $B$ with constant acceleration $( c \mathbf { i } + d \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }$, where $c$ and $d$ are positive constants. The velocity of $P$ at $A$ is $( - 3 \mathbf { i } - 3 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ and the velocity of $P$ at $B$ is $( 2 \mathbf { i } + 9 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$. The magnitude of the acceleration of $P$ is $2.6 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.
\end{enumerate}
Find the value of $c$ and the value of $d$.\\
\hfill \mbox{\textit{Edexcel M1 2015 Q7 [5]}}