OCR MEI M1 2005 June — Question 1 8 marks

Exam BoardOCR MEI
ModuleM1 (Mechanics 1)
Year2005
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVariable acceleration (1D)
TypeVelocity from acceleration by integration
DifficultyModerate -0.8 This is a straightforward mechanics question requiring reading values from a graph, finding area under an acceleration-time graph to get velocity, and understanding that maximum speed occurs when acceleration becomes negative. All parts use standard M1 techniques with no problem-solving insight required—easier than average A-level.
Spec3.02c Interpret kinematic graphs: gradient and area3.02f Non-uniform acceleration: using differentiation and integration
1 A particle travels along a straight line. Its acceleration during the time interval \(0 \leqslant t \leqslant 8\) is given by the acceleration-time graph in Fig. 1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{04848aba-9e64-4265-a4a5-e9336b958a05-2_737_1274_502_461} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure}
  1. Write down the acceleration of the particle when \(t = 4\). Given that the particle starts from rest, find its speed when \(t = 4\).
  2. Write down an expression in terms of \(t\) for the acceleration, \(a \mathrm {~ms} ^ { - 2 }\), of the particle in the time interval \(0 \leqslant t \leqslant 4\).
  3. Without calculation, state the time at which the speed of the particle is greatest. Give a reason for your answer.
  4. Calculate the change in speed of the particle from \(t = 5\) to \(t = 8\), indicating whether this is an increase or a decrease.
1 A particle travels along a straight line. Its acceleration during the time interval $0 \leqslant t \leqslant 8$ is given by the acceleration-time graph in Fig. 1.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{04848aba-9e64-4265-a4a5-e9336b958a05-2_737_1274_502_461}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}

(i) Write down the acceleration of the particle when $t = 4$. Given that the particle starts from rest, find its speed when $t = 4$.\\
(ii) Write down an expression in terms of $t$ for the acceleration, $a \mathrm {~ms} ^ { - 2 }$, of the particle in the time interval $0 \leqslant t \leqslant 4$.\\
(iii) Without calculation, state the time at which the speed of the particle is greatest. Give a reason for your answer.\\
(iv) Calculate the change in speed of the particle from $t = 5$ to $t = 8$, indicating whether this is an increase or a decrease.

\hfill \mbox{\textit{OCR MEI M1 2005 Q1 [8]}}
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