Edexcel M1 2004 November — Question 1

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2004
SessionNovember
TopicSUVAT & Travel Graphs
  1. A man is driving a car on a straight horizontal road. He sees a junction \(S\) ahead, at which he must stop. When the car is at the point \(P , 300 \mathrm {~m}\) from \(S\), its speed is \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The car continues at this constant speed for 2 s after passing \(P\). The man then applies the brakes so that the car has constant deceleration and comes to rest at \(S\).
    1. Sketch, in the space below, a speed-time graph to illustrate the motion of the car in moving from \(P\) to \(S\).
    2. Find the time taken by the car to travel from \(P\) to \(S\).
      (3)
    \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{31c17a67-4fcf-4402-b00e-239ce9f20964-2_421_460_884_758}
    \end{figure} The particles have mass 3 kg and \(m \mathrm {~kg}\), where \(m < 3\). They are attached to the ends of a light inextensible string. The string passes over a smooth fixed pulley. The particles are held in position with the string taut and the hanging parts of the string vertical, as shown in Figure 1. The particles are then released from rest. The initial acceleration of each particle has magnitude \(\frac { 3 } { 7 } g\). Find
  2. the tension in the string immediately after the particles are released,
  3. the value of \(m\). \section*{3.} \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{31c17a67-4fcf-4402-b00e-239ce9f20964-3_241_1202_388_420}
    \end{figure} A plank of wood \(A B\) has mass 10 kg and length 4 m . It rests in a horizontal position on two smooth supports. One support is at the end \(A\). The other is at the point \(C , 0.4 \mathrm {~m}\) from \(B\), as shown in Figure 2. A girl of mass 30 kg stands at \(B\) with the plank in equilibrium. By modelling the plank as a uniform rod and the girl as a particle,
  4. find the reaction on the plank at \(A\). The girl gets off the plank. A boulder of mass \(m \mathrm {~kg}\) is placed on the plank at \(A\) and a man of mass 80 kg stands on the plank at \(B\). The plank remains in equilibrium and is on the point of tilting about \(C\). By modelling the plank again as a uniform rod, and the man and the boulder as particles,
  5. find the value of \(m\).
    (4)
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