| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2023 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Find acceleration from distances/times |
| Difficulty | Moderate -0.3 This is a standard M1 SUVAT question with algebraic parameters requiring systematic application of kinematic equations across two stages. Part (a) is routine 'show that' algebra, part (b) requires linking the two stages, and part (c) needs careful time calculation. While multi-step, it follows predictable M1 patterns without requiring novel insight or particularly challenging manipulation. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(P\) to \(Q\): \(6x = \left(\dfrac{u+2u}{2}\right)12\) OR \(6x = 12u + \dfrac{1}{2} \times \dfrac{u}{12} \times 12^2\) OR \((2u)^2 = u^2 + 2 \times \dfrac{u}{12} \times 6x\) | M1 | Considers \(P\) to \(Q\); forms relevant equation in \(u\) and \(x\) |
| \(x = 3u\) * | A1* | Reaches given answer from correct working |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(Q\) to \(R\): \((3u)^2 = (2u)^2 + 2(1.5)(15u)\) | M1 A1 | Uses given answer from (a) to form equation in \(u\) only; correct unsimplified equation |
| \(u = 9\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(Q\) to \(S\) (\(t=14\) position): \(QS = 2u \times 2 + \dfrac{1}{2} \times 1.5 \times 2^2\) | M1 A1 | Complete method for distance in 2 seconds after \(Q\); correct unsimplified expression in \(u\) only (or 39 m) |
| \((4u+3) + 18u\) | M1 | Complete method for required distance (need \(18u\) or \(6x\)) |
| \(201\) (m) | A1 |
# Question 5:
## Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $P$ to $Q$: $6x = \left(\dfrac{u+2u}{2}\right)12$ OR $6x = 12u + \dfrac{1}{2} \times \dfrac{u}{12} \times 12^2$ OR $(2u)^2 = u^2 + 2 \times \dfrac{u}{12} \times 6x$ | M1 | Considers $P$ to $Q$; forms relevant equation in $u$ and $x$ |
| $x = 3u$ * | A1* | Reaches given answer from correct working |
## Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $Q$ to $R$: $(3u)^2 = (2u)^2 + 2(1.5)(15u)$ | M1 A1 | Uses given answer from (a) to form equation in $u$ only; correct unsimplified equation |
| $u = 9$ | A1 | |
## Part (c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $Q$ to $S$ ($t=14$ position): $QS = 2u \times 2 + \dfrac{1}{2} \times 1.5 \times 2^2$ | M1 A1 | Complete method for distance in 2 seconds after $Q$; correct unsimplified expression in $u$ only (or 39 m) |
| $(4u+3) + 18u$ | M1 | Complete method for required distance (need $18u$ or $6x$) |
| $201$ (m) | A1 | |
---5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{84c0eead-0a87-4d87-b33d-794a94bb466c-14_117_1393_328_337}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
Three points $P , Q$ and $R$ are on a horizontal road where $P Q R$ is a straight line.\\
The point $Q$ is between $P$ and $R$, with $P Q = 6 x$ metres and $Q R = 5 x$ metres, as shown in Figure 2.
A vehicle moves along the road from $P$ to $Q$ with constant acceleration.\\
The vehicle is modelled as a particle.\\
At time $t = 0$, the vehicle passes $P$ with speed $u \mathrm {~ms} ^ { - 1 }$\\
At time $t = 12 \mathrm {~s}$, the vehicle passes $Q$ with speed $2 u \mathrm {~ms} ^ { - 1 }$\\
Using the model,
\begin{enumerate}[label=(\alph*)]
\item show that $x = 3 u$
As the vehicle passes $Q$, the acceleration of the vehicle changes instantaneously to $1.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$
The vehicle continues to move with a constant acceleration of $1.5 \mathrm {~ms} ^ { - 2 }$ and passes $R$ with speed $3 u \mathrm {~ms} ^ { - 1 }$
Using the model,
\item find the value of $u$,
\item find the distance travelled by the vehicle during the first 14 seconds after passing $P$
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2023 Q5 [9]}}