Edexcel M1 2012 January — Question 6 13 marks

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2012
SessionJanuary
Marks13
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Mark schemeDownload PDF ↗
TopicConstant acceleration (SUVAT)
TypeMulti-phase journey: find unknown speed or time
DifficultyModerate -0.3 This is a standard M1 SUVAT question with three stages of motion requiring systematic application of kinematic equations. While it involves algebraic unknowns (T and a) and multiple parts, the problem-solving approach is straightforward and methodical—students work through each stage sequentially using v=u+at and s=ut+½at². The deceleration time calculation is direct, finding T requires setting up one equation from total distance, and a follows immediately. This is slightly easier than average because it's a textbook multi-stage motion problem with clear structure and no conceptual surprises.
Spec3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae

  1. A car moves along a straight horizontal road from a point \(A\) to a point \(B\), where \(A B = 885 \mathrm {~m}\). The car accelerates from rest at \(A\) to a speed of \(15 \mathrm {~ms} ^ { - 1 }\) at a constant rate \(a \mathrm {~ms} ^ { - 2 }\). The time for which the car accelerates is \(\frac { 1 } { 3 } T\) seconds. The car maintains the speed of \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for \(T\) seconds. The car then decelerates at a constant rate of \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) stopping at \(B\).
    1. Find the time for which the car decelerates.
    2. Sketch a speed-time graph for the motion of the car.
    3. Find the value of \(T\).
    4. Find the value of \(a\).
    5. Sketch an acceleration-time graph for the motion of the car.

\begin{enumerate}
  \item A car moves along a straight horizontal road from a point $A$ to a point $B$, where $A B = 885 \mathrm {~m}$. The car accelerates from rest at $A$ to a speed of $15 \mathrm {~ms} ^ { - 1 }$ at a constant rate $a \mathrm {~ms} ^ { - 2 }$. The time for which the car accelerates is $\frac { 1 } { 3 } T$ seconds. The car maintains the speed of $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ for $T$ seconds. The car then decelerates at a constant rate of $2.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ stopping at $B$.\\
(a) Find the time for which the car decelerates.\\
(b) Sketch a speed-time graph for the motion of the car.\\
(c) Find the value of $T$.\\
(d) Find the value of $a$.\\
(e) Sketch an acceleration-time graph for the motion of the car.\\

\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2012 Q6 [13]}}