| Exam Board | Edexcel |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2021 |
| Session | October |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Constant acceleration vector (i and j) |
| Difficulty | Moderate -0.8 This is a straightforward application of SUVAT equations in vector form with no problem-solving required. Part (a) uses v = u + at directly, and part (b) uses s = ut + ½at². Both are routine calculations with given values, requiring only substitution and basic vector arithmetic—easier than average A-level questions. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10h Vectors in kinematics: uniform acceleration in vector form3.02e Two-dimensional constant acceleration: with vectors3.02g Two-dimensional variable acceleration |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Use of \(\mathbf{v} = \mathbf{u} + \mathbf{a}t\) with \(t=2\): \(\mathbf{v} = 4\mathbf{i} + 2(2\mathbf{i}-3\mathbf{j})\) OR integration: \(\mathbf{v} = (2\mathbf{i}-3\mathbf{j})t + 4\mathbf{i}\), with \(t=2\) | M1 | Complete method to find v, using ruva\(t\) or integration. M0 if i and/or j is missing |
| \(\mathbf{v} = 8\mathbf{i} - 6\mathbf{j}\) | A1 | Apply isw if they also find the speed |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Use of \(\mathbf{r} = \mathbf{u}t + \frac{1}{2}\mathbf{a}t^2\) at \(t=3\): \((\mathbf{i}+\mathbf{j}) + \left[3\times4\mathbf{i}+\frac{1}{2}\times(2\mathbf{i}-3\mathbf{j})\times3^2\right]\) OR find v at \(t=3\): \(4\mathbf{i}+3(2\mathbf{i}-3\mathbf{j})=(10\mathbf{i}-9\mathbf{j})\) then use \(\mathbf{r}=\frac{1}{2}(\mathbf{u}+\mathbf{v})t\): \((\mathbf{i}+\mathbf{j})+\left[\frac{1}{2}[4\mathbf{i}+(10\mathbf{i}-9\mathbf{j})]\times3\right]\) OR \(\mathbf{r} = \mathbf{v}t - \frac{1}{2}\mathbf{a}t^2\): \((\mathbf{i}+\mathbf{j})+\left[3\times(10\mathbf{i}-9\mathbf{j})-\frac{1}{2}\times(2\mathbf{i}-3\mathbf{j})\times3^2\right]\) OR integration: \(\mathbf{r} = (\mathbf{i}+\mathbf{j})+\left[(2\mathbf{i}-3\mathbf{j})\frac{1}{2}t^2+4t\mathbf{i}\right]\), with \(t=3\) | M1 | Complete method to find p.v. M1 scored if they omit \((\mathbf{i}+\mathbf{j})\), i.e. M1 is for expression in square bracket. If they integrate, M1 earned once expression in square bracket seen with \(t=3\). M0 if i and/or j missing |
| \(\mathbf{r} = 22\mathbf{i} - 12.5\mathbf{j}\) | A1 | cao |
## Question 1:
### Part 1(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Use of $\mathbf{v} = \mathbf{u} + \mathbf{a}t$ with $t=2$: $\mathbf{v} = 4\mathbf{i} + 2(2\mathbf{i}-3\mathbf{j})$ **OR** integration: $\mathbf{v} = (2\mathbf{i}-3\mathbf{j})t + 4\mathbf{i}$, with $t=2$ | M1 | Complete method to find **v**, using **ruva**$t$ or integration. M0 if **i** and/or **j** is missing |
| $\mathbf{v} = 8\mathbf{i} - 6\mathbf{j}$ | A1 | Apply isw if they also find the speed |
### Part 1(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Use of $\mathbf{r} = \mathbf{u}t + \frac{1}{2}\mathbf{a}t^2$ at $t=3$: $(\mathbf{i}+\mathbf{j}) + \left[3\times4\mathbf{i}+\frac{1}{2}\times(2\mathbf{i}-3\mathbf{j})\times3^2\right]$ **OR** find **v** at $t=3$: $4\mathbf{i}+3(2\mathbf{i}-3\mathbf{j})=(10\mathbf{i}-9\mathbf{j})$ then use $\mathbf{r}=\frac{1}{2}(\mathbf{u}+\mathbf{v})t$: $(\mathbf{i}+\mathbf{j})+\left[\frac{1}{2}[4\mathbf{i}+(10\mathbf{i}-9\mathbf{j})]\times3\right]$ **OR** $\mathbf{r} = \mathbf{v}t - \frac{1}{2}\mathbf{a}t^2$: $(\mathbf{i}+\mathbf{j})+\left[3\times(10\mathbf{i}-9\mathbf{j})-\frac{1}{2}\times(2\mathbf{i}-3\mathbf{j})\times3^2\right]$ **OR integration:** $\mathbf{r} = (\mathbf{i}+\mathbf{j})+\left[(2\mathbf{i}-3\mathbf{j})\frac{1}{2}t^2+4t\mathbf{i}\right]$, with $t=3$ | M1 | Complete method to find p.v. M1 scored if they omit $(\mathbf{i}+\mathbf{j})$, i.e. M1 is for expression in square bracket. If they integrate, M1 earned once expression in square bracket seen with $t=3$. M0 if **i** and/or **j** missing |
| $\mathbf{r} = 22\mathbf{i} - 12.5\mathbf{j}$ | A1 | cao |
---\begin{enumerate}
\item A particle $P$ moves with constant acceleration $( 2 \mathbf { i } - 3 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }$
\end{enumerate}
At time $t = 0 , P$ is moving with velocity $4 \mathbf { i } \mathrm {~m} \mathrm {~s} ^ { - 1 }$\\
(a) Find the velocity of $P$ at time $t = 2$ seconds.
At time $t = 0$, the position vector of $P$ relative to a fixed origin $O$ is $( \mathbf { i } + \mathbf { j } ) \mathrm { m }$.\\
(b) Find the position vector of $P$ relative to $O$ at time $t = 3$ seconds.
\hfill \mbox{\textit{Edexcel Paper 3 2021 Q1 [4]}}