| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2009 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Constant acceleration with algebraic unknowns |
| Difficulty | Moderate -0.3 This is a straightforward kinematics problem using SUVAT equations with constant acceleration. Students need to set up two equations from the given distances and times, then solve simultaneously for u and a. While it requires careful algebraic manipulation, it's a standard M1 exercise with no conceptual surprises—slightly easier than average due to its routine nature. |
| Spec | 3.02a Kinematics language: position, displacement, velocity, acceleration3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks |
|---|---|
| \(45 = 2u + \frac{1}{2}a \cdot 2^2 \Rightarrow 45 = 2u + 2a\) | M1 A1 |
| \(165 = 6u + \frac{1}{2}a \cdot 6^2 \Rightarrow 165 = 6u + 18a\) | M1 A1 |
| Eliminating either \(u\) or \(a\) | M1 |
| \(u = 20\) and \(a = 2.5\) | A1 A1 |
| Total: [7] |
$45 = 2u + \frac{1}{2}a \cdot 2^2 \Rightarrow 45 = 2u + 2a$ | M1 A1 |
$165 = 6u + \frac{1}{2}a \cdot 6^2 \Rightarrow 165 = 6u + 18a$ | M1 A1 |
Eliminating either $u$ or $a$ | M1 |
$u = 20$ and $a = 2.5$ | A1 A1 |
| **Total: [7]** |Three posts $P$, $Q$ and $R$ are fixed in that order at the side of a straight horizontal road. The distance from $P$ to $Q$ is 45 m and the distance from $Q$ to $R$ is 120 m. A car is moving along the road with constant acceleration $a$ m s$^{-2}$. The speed of the car, as it passes $P$, is $u$ m s$^{-1}$. The car passes $Q$ two seconds after passing $P$, and the car passes $R$ four seconds after passing $Q$. Find
\begin{enumerate}[label=(\roman*)]
\item the value of $u$,
\item the value of $a$.
\end{enumerate}
[7]
\hfill \mbox{\textit{Edexcel M1 2009 Q1 [7]}}