| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 11 |
| 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 kinematics question requiring basic calculations of time from distance/speed, sketching a displacement-time graph with three linear segments, and finding an intersection point. All techniques are routine M1 content with no conceptual challenges or novel problem-solving required. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time |
A man travels $360$ m along a straight road. He walks for the first $120$ m at $1.5$ m s$^{-1}$, runs the next $180$ m at $4.5$ m s$^{-1}$, and then walks the final $60$ m at $1.5$ m s$^{-1}$. The man's displacement from his starting point after $t$ seconds is $x$ metres.
\begin{enumerate}[label=(\roman*)]
\item Sketch the $(t, x)$ graph for the journey, showing the values of $t$ for which $x = 120, 300$ and $360$. [5]
\end{enumerate}
A woman jogs the same $360$ m route at constant speed, starting at the same instant as the man and finishing at the same instant as the man.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Draw a dotted line on your $(t, x)$ graph to represent the woman's journey. [1]
\item Calculate the value of $t$ at which the man overtakes the woman. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q3 [11]}}