| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | SUVAT simultaneous equations: find u and a |
| Difficulty | Standard +0.3 This is a two-stage SUVAT problem requiring students to set up equations for each phase and solve simultaneously for the unknown time t. While it involves multiple steps and algebraic manipulation, it follows a standard M1 pattern with clearly defined stages and straightforward application of kinematic equations. Slightly above average due to the algebraic component and two-phase structure, but well within typical M1 scope. |
| Spec | 3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (a) At \(P\), \(v = 9 + 3.6t\) | M1 A1 | |
| At \(Q\), \(v = 9 + 3.6t + 2t = 9 + 5.6t\) | M1 A1 | |
| \(9 + 5.6t = 16\) | ||
| \(5.6t = 7\) | ||
| \(t = 1.25\) | ||
| \(O\) to \(Q\): 2.5 s | M1 A1 | |
| (b) \(\frac{1}{2} \times 1.25 \times (9 + 13.5 + 13.5 + 16) = 32.5\) m | M1 A1 A1 | Total: 7 marks |
**(a)** At $P$, $v = 9 + 3.6t$ | M1 A1 |
At $Q$, $v = 9 + 3.6t + 2t = 9 + 5.6t$ | M1 A1 |
$9 + 5.6t = 16$ | |
$5.6t = 7$ | |
$t = 1.25$ | |
$O$ to $Q$: 2.5 s | | M1 A1 |
**(b)** $\frac{1}{2} \times 1.25 \times (9 + 13.5 + 13.5 + 16) = 32.5$ m | M1 A1 A1 | **Total: 7 marks**2. A particle passes through a point $O$ with speed $9 \mathrm {~ms} ^ { - 1 }$ and moves in a straight line with constant acceleration $3.6 \mathrm {~ms} ^ { - 2 }$ for $t$ seconds until it reaches the point $P$. The acceleration is then reduced to $2 \mathrm {~ms} ^ { - 2 }$ and this is maintained for another $t$ seconds until the particle passes the point $Q$ with speed $16 \mathrm {~ms} ^ { - 1 }$. Calculate
\begin{enumerate}[label=(\alph*)]
\item the time taken by the particle to travel from $O$ to $Q$,
\item the distance $O Q$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q2 [7]}}