| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Displacement-time graph interpretation or sketching |
| Difficulty | Moderate -0.8 This is a straightforward M1 kinematics question requiring students to read gradients from a displacement-time graph, calculate distances, write a linear equation, and sketch a velocity-time graph. All parts involve standard techniques with no problem-solving insight required—primarily testing understanding of the relationship between displacement, velocity, and graph gradients at an introductory mechanics level. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area |
| Answer | Marks | Guidance |
|---|---|---|
| (a) (i) \(1.5\) ms\(^{-1}\) | B1 | |
| (ii) \(-1\frac{1}{3}\) ms\(^{-1}\) | B1 | |
| (b) \(2 \times 7\) m \(= 14\) m | M1 A1 | |
| (c) Line from \((2, 3)\) to \((4, 7)\) is \(y - 3 = 2(t - 2)\) → \(y = 2t - 1\) | M1 A1 A1 | |
| (d) Graph sketched: 6 horizontal line segments | B3 | |
| (e) Steepest section has gradient \(-3\), so max. speed \(= 3\) ms\(^{-1}\) | M1 A1 A1 | Total: 13 marks |
**(a)** (i) $1.5$ ms$^{-1}$ | B1 |
(ii) $-1\frac{1}{3}$ ms$^{-1}$ | B1 |
**(b)** $2 \times 7$ m $= 14$ m | M1 A1 |
**(c)** Line from $(2, 3)$ to $(4, 7)$ is $y - 3 = 2(t - 2)$ → $y = 2t - 1$ | M1 A1 A1 |
**(d)** Graph sketched: 6 horizontal line segments | B3 |
**(e)** Steepest section has gradient $-3$, so max. speed $= 3$ ms$^{-1}$ | M1 A1 A1 | **Total: 13 marks**A particle $P$ moves in a straight line such that its displacement from a fixed point $O$ at time $t$ s is $y$ metres. The graph of $y$ against $t$ is as shown.
\begin{tikzpicture}[>=latex]
% Grid
\draw[gray, thin] (0,0) grid (12,8);
% Axes
\draw[thick,->] (0,0) -- (12.6,0) node[right] {$t$\,(s)};
\draw[thick,->] (0,0) -- (0,8.6) node[above left] {$y$\,(m)};
% x-axis tick labels
\foreach \x in {0,1,...,12}
\node[below] at (\x,0) {\x};
% y-axis tick labels
\foreach \y in {0,1,...,8}
\node[left] at (0,\y) {\y};
% The graph
\draw[very thick] (0,0) -- (2,3) -- (4,7) -- (7,7) -- (8,4) -- (9,4) -- (12,0);
\end{tikzpicture}
\begin{enumerate}[label=(\alph*)]
\item Write down the velocity of $P$ when
\begin{enumerate}[label=(\roman*)]
\item $t = 1$, \quad (ii) $t = 10$. \hfill [2 marks]
\end{enumerate}
\item State the total distance travelled by $P$. \hfill [2 marks]
\item Write down a formula for $y$ in terms of $t$ when $2 \leq t < 4$. \hfill [3 marks]
\item Sketch a velocity-time graph for the motion of $P$ during the twelve seconds. \hfill [3 marks]
\item Find the maximum speed of $P$ during the motion. \hfill [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q6 [13]}}