OCR M1 — Question 3 11 marks

Exam BoardOCR
ModuleM1 (Mechanics 1)
Marks11
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTravel graphs
TypeDisplacement-time graph interpretation or sketching
DifficultyModerate -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.
Spec3.02b 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.
  1. Sketch the \((t, x)\) graph for the journey, showing the values of \(t\) for which \(x = 120, 300\) and \(360\). [5]
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.
  1. Draw a dotted line on your \((t, x)\) graph to represent the woman's journey. [1]
  2. Calculate the value of \(t\) at which the man overtakes the woman. [5]

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]}}