| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Time to reach midpoint or specific position |
| Difficulty | Moderate -0.8 This is a straightforward M1 kinematics and dynamics question requiring standard SUVAT equations and Newton's second law. Parts (a)-(c) involve routine application of kinematic formulae with given values, while part (d) is a direct F=ma calculation. No problem-solving insight or complex reasoning is needed—just methodical application of well-practiced techniques. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03c Newton's second law: F=ma one dimension |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(420 = \frac{1}{2}(20 + 8)t\) where \(t = 30\) s | M1 A1 | |
| (b) \(20 = 8 + 30a\) where \(30a = 12\) and \(a = 0.4\) ms\(^{-2}\) | M1 A1 | |
| (c) \(s = ut + \frac{1}{2}at^2\); \(240 = 8t + 0.2t^2\) | M1 A1 | |
| \(t^2 + 40t - 1200 = 0\) | M1 A1 | |
| \((t - 20)(t + 60) = 0\) where \(t = 20\) | M1 A1 | |
| (d) \(F = ma\); \(900 - R = 1200(0.4)\) where \(R = 900 - 480 = 420\) N | M1 A1 A1 | Total: 11 marks |
**(a)** $420 = \frac{1}{2}(20 + 8)t$ where $t = 30$ s | M1 A1 |
**(b)** $20 = 8 + 30a$ where $30a = 12$ and $a = 0.4$ ms$^{-2}$ | M1 A1 |
**(c)** $s = ut + \frac{1}{2}at^2$; $240 = 8t + 0.2t^2$ | M1 A1 |
$t^2 + 40t - 1200 = 0$ | M1 A1 |
$(t - 20)(t + 60) = 0$ where $t = 20$ | M1 A1 |
**(d)** $F = ma$; $900 - R = 1200(0.4)$ where $R = 900 - 480 = 420$ N | M1 A1 A1 | **Total: 11 marks**A car moves in a straight line from $P$ to $Q$, a distance of $420$ m, with constant acceleration. At $P$ the speed of the car is $8$ ms$^{-1}$. At $Q$ the speed of the car is $20$ ms$^{-1}$. Find
\begin{enumerate}[label=(\alph*)]
\item the time taken to travel from $P$ to $Q$, \hfill [2 marks]
\item the acceleration of the car, \hfill [2 marks]
\item the time taken for the car to travel $240$ m from $P$. \hfill [4 marks]
\end{enumerate}
Given that the mass of the car is $1200$ kg and the tractive force of the car is $900$ N,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item find the magnitude of the resistance to the car's motion. \hfill [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [11]}}