Questions M1 (1912 questions)

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AQA AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Paper 1 Further Paper 2 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics M1 M2 M3 Paper 1 Paper 2 Paper 3 S1 S2 S3 CAIE FP1 FP2 Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 4 M1 M2 P1 P2 P3 S1 S2 Edexcel AEA AS Paper 1 AS Paper 2 C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS M1 M2 M3 M4 M5 P1 P2 P3 P4 PMT Mocks Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 OCR AS Pure C1 C2 C3 C4 D1 D2 FD1 AS FM1 AS FP1 FP1 AS FP2 FP3 FS1 AS Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Mechanics Further Mechanics AS Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Statistics Further Statistics AS H240/01 H240/02 H240/03 M1 M2 M3 M4 Mechanics 1 PURE Pure 1 S1 S2 S3 S4 Stats 1 OCR MEI AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further Extra Pure Further Mechanics A AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Pure Core Further Pure Core AS Further Pure with Technology Further Statistics A AS Further Statistics B AS Further Statistics Major Further Statistics Minor M1 M2 M3 M4 Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 SPS SPS ASFM SPS ASFM Mechanics SPS ASFM Pure SPS ASFM Statistics SPS FM SPS FM Mechanics SPS FM Pure SPS FM Statistics SPS SM SPS SM Mechanics SPS SM Pure SPS SM Statistics WJEC Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 Unit 1 Unit 2 Unit 3 Unit 4
Edexcel M1 2014 June Q2
7 marks Moderate -0.3
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ed659098-c1cf-4ee1-a12a-bf8b6c42db95-03_435_840_269_561} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A rough plane is inclined at \(40 ^ { \circ }\) to the horizontal. Two points \(A\) and \(B\) are 3 metres apart and lie on a line of greatest slope of the inclined plane, with \(A\) above \(B\), as shown in Figure 2. A particle \(P\) of mass \(m \mathrm {~kg}\) is held at rest on the plane at \(A\). The coefficient of friction between \(P\) and the plane is \(\frac { 1 } { 2 }\). The particle is released.
  1. Find the acceleration of \(P\) down the plane.
  2. Find the speed of \(P\) at \(B\).
Edexcel M1 2014 June Q3
13 marks Moderate -0.8
  1. A ball of mass 0.3 kg is released from rest at a point which is 2 m above horizontal ground. The ball moves freely under gravity. After striking the ground, the ball rebounds vertically and rises to a maximum height of 1.5 m above the ground, before falling to the ground again. The ball is modelled as a particle.
    1. Find the speed of the ball at the instant before it strikes the ground for the first time.
    2. Find the speed of the ball at the instant after it rebounds from the ground for the first time.
    3. Find the magnitude of the impulse on the ball in the first impact with the ground.
    4. Sketch, in the space provided, a velocity-time graph for the motion of the ball from the instant when it is released until the instant when it strikes the ground for the second time.
    5. Find the time between the instant when the ball is released and the instant when it strikes the ground for the second time.
Edexcel M1 2014 June Q4
12 marks Moderate -0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ed659098-c1cf-4ee1-a12a-bf8b6c42db95-07_513_993_276_479} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A beam \(A B\) has weight \(W\) newtons and length 4 m . The beam is held in equilibrium in a horizontal position by two vertical ropes attached to the beam. One rope is attached to \(A\) and the other rope is attached to the point \(C\) on the beam, where \(A C = d\) metres, as shown in Figure 3. The beam is modelled as a uniform rod and the ropes as light inextensible strings. The tension in the rope attached at \(C\) is double the tension in the rope attached at \(A\).
  1. Find the value of \(d\). A small load of weight \(k W\) newtons is attached to the beam at \(B\). The beam remains in equilibrium in a horizontal position. The load is modelled as a particle. The tension in the rope attached at \(C\) is now four times the tension in the rope attached at \(A\).
  2. Find the value of \(k\).
Edexcel M1 2014 June Q5
12 marks Moderate -0.3
5. A particle \(P\) of mass 0.5 kg is moving under the action of a single force \(( 3 \mathbf { i } - 2 \mathbf { j } ) \mathrm { N }\).
  1. Show that the magnitude of the acceleration of \(P\) is \(2 \sqrt { 13 } \mathrm {~m} \mathrm {~s} ^ { - 2 }\). At time \(t = 0\), the velocity of \(P\) is \(( \mathbf { i } + 3 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
  2. Find the velocity of \(P\) at time \(t = 2\) seconds. Another particle \(Q\) moves with constant velocity \(\mathbf { v } = ( 2 \mathbf { i } - \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
  3. Find the distance moved by \(Q\) in 2 seconds.
  4. Show that at time \(t = 3.5\) seconds both particles are moving in the same direction.
Edexcel M1 2014 June Q6
9 marks Moderate -0.3
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ed659098-c1cf-4ee1-a12a-bf8b6c42db95-11_472_908_285_520} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Two forces \(\mathbf { P }\) and \(\mathbf { Q }\) act on a particle at \(O\). The angle between the lines of action of \(\mathbf { P }\) and \(\mathbf { Q }\) is \(120 ^ { \circ }\) as shown in Figure 4. The force \(\mathbf { P }\) has magnitude 20 N and the force \(\mathbf { Q }\) has magnitude \(X\) newtons. The resultant of \(\mathbf { P }\) and \(\mathbf { Q }\) is the force \(\mathbf { R }\). Given that the magnitude of \(\mathbf { R }\) is \(3 X\) newtons, find, giving your answers to 3 significant figures
  1. the value of \(X\),
  2. the magnitude of \(( \mathbf { P } - \mathbf { Q } )\).
Edexcel M1 2014 June Q7
16 marks Standard +0.3
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ed659098-c1cf-4ee1-a12a-bf8b6c42db95-13_490_316_267_815} \captionsetup{labelformat=empty} \caption{Figure 5}
\end{figure} Three particles \(A , B\) and \(C\) have masses \(3 m , 2 m\) and \(2 m\) respectively. Particle \(C\) is attached to particle \(B\). Particles \(A\) and \(B\) are connected by a light inextensible string which passes over a smooth light fixed pulley. The system is held at rest with the string taut and the hanging parts of the string vertical, as shown in Figure 5. The system is released from rest and \(A\) moves upwards.
    1. Show that the acceleration of \(A\) is \(\frac { g } { 7 }\)
    2. Find the tension in the string as \(A\) ascends. At the instant when \(A\) is 0.7 m above its original position, \(C\) separates from \(B\) and falls away. In the subsequent motion, \(A\) does not reach the pulley.
  2. Find the speed of \(A\) at the instant when it is 0.7 m above its original position.
  3. Find the acceleration of \(A\) at the instant after \(C\) separates from \(B\).
  4. Find the greatest height reached by \(A\) above its original position.
    \includegraphics[max width=\textwidth, alt={}, center]{ed659098-c1cf-4ee1-a12a-bf8b6c42db95-14_115_161_2455_1784}
Edexcel M1 2015 June Q1
6 marks Moderate -0.5
  1. Particle \(P\) of mass \(m\) and particle \(Q\) of mass \(k m\) are moving in opposite directions on a smooth horizontal plane when they collide directly. Immediately before the collision the speed of \(P\) is \(5 u\) and the speed of \(Q\) is \(u\). Immediately after the collision the speed of each particle is halved and the direction of motion of each particle is reversed.
Find
  1. the value of \(k\),
  2. the magnitude of the impulse exerted on \(P\) by \(Q\) in the collision.
Edexcel M1 2015 June Q2
7 marks Moderate -0.8
2. A small stone is projected vertically upwards from a point \(O\) with a speed of \(19.6 \mathrm {~ms} ^ { - 1 }\). Modelling the stone as a particle moving freely under gravity,
  1. find the greatest height above \(O\) reached by the stone,
  2. find the length of time for which the stone is more than 14.7 m above \(O\).
Edexcel M1 2015 June Q3
7 marks Moderate -0.3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{de3245a7-cf6e-423e-8689-9a074bdbc23b-04_540_958_116_482} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A particle of mass 2 kg is suspended from a horizontal ceiling by two light inextensible strings, \(P R\) and \(Q R\). The particle hangs at \(R\) in equilibrium, with the strings in a vertical plane. The string \(P R\) is inclined at \(55 ^ { \circ }\) to the horizontal and the string \(Q R\) is inclined at \(35 ^ { \circ }\) to the horizontal, as shown in Figure 1. \section*{Find}
  1. the tension in the string \(P R\),
  2. the tension in the string \(Q R\).
Edexcel M1 2015 June Q4
7 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{de3245a7-cf6e-423e-8689-9a074bdbc23b-06_428_373_246_788} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A lift of mass 200 kg is being lowered into a mineshaft by a vertical cable attached to the top of the lift. A crate of mass 55 kg is on the floor inside the lift, as shown in Figure 2. The lift descends vertically with constant acceleration. There is a constant upwards resistance of magnitude 150 N on the lift. The crate experiences a constant normal reaction of magnitude 473 N from the floor of the lift.
  1. Find the acceleration of the lift.
  2. Find the magnitude of the force exerted on the lift by the cable.
Edexcel M1 2015 June Q5
12 marks Moderate -0.3
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{de3245a7-cf6e-423e-8689-9a074bdbc23b-08_582_1230_271_374} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A beam \(A B\) has length 5 m and mass 25 kg . The beam is suspended in equilibrium in a horizontal position by two vertical ropes. One rope is attached to the beam at \(A\) and the other rope is attached to the point \(C\) on the beam where \(C B = 0.5 \mathrm {~m}\), as shown in Figure 3. A particle \(P\) of mass 60 kg is attached to the beam at \(B\) and the beam remains in equilibrium in a horizontal position. The beam is modelled as a uniform rod and the ropes are modelled as light strings.
  1. Find
    1. the tension in the rope attached to the beam at \(A\),
    2. the tension in the rope attached to the beam at \(C\). Particle \(P\) is removed and replaced by a particle \(Q\) of mass \(M \mathrm {~kg}\) at \(B\). Given that the beam remains in equilibrium in a horizontal position,
  2. find
    1. the greatest possible value of \(M\),
    2. the greatest possible tension in the rope attached to the beam at \(C\).
Edexcel M1 2015 June Q6
8 marks Easy -1.3
  1. A particle \(P\) is moving with constant velocity. The position vector of \(P\) at time \(t\) seconds \(( t \geqslant 0 )\) is \(\mathbf { r }\) metres, relative to a fixed origin \(O\), and is given by
$$\mathbf { r } = ( 2 t - 3 ) \mathbf { i } + ( 4 - 5 t ) \mathbf { j }$$
  1. Find the initial position vector of \(P\). The particle \(P\) passes through the point with position vector \(( 3.4 \mathbf { i } - 12 \mathbf { j } )\) m at time \(T\) seconds.
  2. Find the value of \(T\).
  3. Find the speed of \(P\).
Edexcel M1 2015 June Q7
13 marks Standard +0.3
7. A train travels along a straight horizontal track between two stations, \(A\) and \(B\). The train starts from rest at \(A\) and moves with constant acceleration \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) until it reaches a speed of \(V \mathrm {~ms} ^ { - 1 } , ( V < 50 )\). The train then travels at this constant speed before it moves with constant deceleration \(0.25 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) until it comes to rest at \(B\).
  1. Sketch in the space below a speed-time graph for the motion of the train between the two stations \(A\) and \(B\). The total time for the journey from \(A\) to \(B\) is 5 minutes.
  2. Find, in terms of \(V\), the length of time, in seconds, for which the train is
    1. accelerating,
    2. decelerating,
    3. moving with constant speed. Given that the distance between the two stations \(A\) and \(B\) is 6.3 km ,
  3. find the value of \(V\).
Edexcel M1 2015 June Q8
15 marks Standard +0.3
8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{de3245a7-cf6e-423e-8689-9a074bdbc23b-14_643_931_118_534} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Two particles \(P\) and \(Q\) have mass 4 kg and 0.5 kg respectively. The particles are attached to the ends of a light inextensible string. Particle \(P\) is held at rest on a fixed rough plane, which is inclined to the horizontal at an angle \(\alpha\) where \(\tan \alpha = \frac { 4 } { 3 }\). The coefficient of friction between \(P\) and the plane is 0.5 . The string lies along the plane and passes over a small smooth light pulley which is fixed at the top of the plane. Particle \(Q\) hangs freely at rest vertically below the pulley. The string lies in the vertical plane which contains the pulley and a line of greatest slope of the inclined plane, as shown in Figure 4. Particle \(P\) is released from rest with the string taut and slides down the plane. Given that \(Q\) has not hit the pulley, find
  1. the tension in the string during the motion,
  2. the magnitude of the resultant force exerted by the string on the pulley.
Edexcel M1 2016 June Q1
10 marks Moderate -0.3
  1. \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors due east and due north respectively and position vectors are given relative to a fixed origin \(O\).]
Two cars \(P\) and \(Q\) are moving on straight horizontal roads with constant velocities. The velocity of \(P\) is \(( 15 \mathbf { i } + 20 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) and the velocity of \(Q\) is \(( 20 \mathbf { i } - 5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\)
  1. Find the direction of motion of \(Q\), giving your answer as a bearing to the nearest degree. At time \(t = 0\), the position vector of \(P\) is \(400 \mathbf { i }\) metres and the position vector of \(Q\) is 800j metres. At time \(t\) seconds, the position vectors of \(P\) and \(Q\) are \(\mathbf { p }\) metres and \(\mathbf { q }\) metres respectively.
  2. Find an expression for
    1. \(\mathbf { p }\) in terms of \(t\),
    2. \(\mathbf { q }\) in terms of \(t\).
  3. Find the position vector of \(Q\) when \(Q\) is due west of \(P\).
Edexcel M1 2016 June Q2
6 marks Moderate -0.8
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d408dd83-c5b2-4e55-b5c1-3e7f3faadbcb-04_327_255_283_847} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A vertical rope \(A B\) has its end \(B\) attached to the top of a scale pan. The scale pan has mass 0.5 kg and carries a brick of mass 1.5 kg , as shown in Figure 1. The scale pan is raised vertically upwards with constant acceleration \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) using the rope \(A B\). The rope is modelled as a light inextensible string.
  1. Find the tension in the rope \(A B\).
  2. Find the magnitude of the force exerted on the scale pan by the brick.
Edexcel M1 2016 June Q3
7 marks Standard +0.3
3. A particle \(P\) of mass 0.4 kg is moving on rough horizontal ground when it hits a fixed vertical plane wall. Immediately before hitting the wall, \(P\) is moving with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in a direction perpendicular to the wall. The particle rebounds from the wall and comes to rest at a distance of 5 m from the wall. The coefficient of friction between \(P\) and the ground is \(\frac { 1 } { 8 }\). Find the magnitude of the impulse exerted on \(P\) by the wall.
Edexcel M1 2016 June Q4
12 marks Moderate -0.3
4. Two trains \(M\) and \(N\) are moving in the same direction along parallel straight horizontal tracks. At time \(t = 0 , M\) overtakes \(N\) whilst they are travelling with speeds \(40 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively. Train \(M\) overtakes train \(N\) as they pass a point \(X\) at the side of the tracks. After overtaking \(N\), train \(M\) maintains its speed of \(40 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for \(T\) seconds and then decelerates uniformly, coming to rest next to a point \(Y\) at the side of the tracks. After being overtaken, train \(N\) maintains its speed of \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for 25 s and then decelerates uniformly, also coming to rest next to the point \(Y\). The times taken by the trains to travel between \(X\) and \(Y\) are the same.
  1. Sketch, on the same diagram, the speed-time graphs for the motions of the two trains between \(X\) and \(Y\). Given that \(X Y = 975 \mathrm {~m}\),
  2. find the value of \(T\).
Edexcel M1 2016 June Q5
10 marks Standard +0.3
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d408dd83-c5b2-4e55-b5c1-3e7f3faadbcb-08_321_917_285_518} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A particle \(P\) of mass 2 kg is held at rest in equilibrium on a rough plane by a constant force of magnitude 40 N . The direction of the force is inclined to the plane at an angle of \(30 ^ { \circ }\). The plane is inclined to the horizontal at an angle of \(20 ^ { \circ }\), as shown in Figure 2. The line of action of the force lies in the vertical plane containing \(P\) and a line of greatest slope of the plane. The coefficient of friction between \(P\) and the plane is \(\mu\). Given that \(P\) is on the point of sliding up the plane, find the value of \(\mu\).
Edexcel M1 2016 June Q6
7 marks Standard +0.3
6. A non-uniform plank \(A B\) has length 6 m and mass 30 kg . The plank rests in equilibrium in a horizontal position on supports at the points \(S\) and \(T\) of the plank where \(A S = 0.5 \mathrm {~m}\) and \(T B = 2 \mathrm {~m}\). When a block of mass \(M \mathrm {~kg}\) is placed on the plank at \(A\), the plank remains horizontal and in equilibrium and the plank is on the point of tilting about \(S\). When the block is moved to \(B\), the plank remains horizontal and in equilibrium and the plank is on the point of tilting about \(T\). The distance of the centre of mass of the plank from \(A\) is \(d\) metres. The block is modelled as a particle and the plank is modelled as a non-uniform rod. Find
  1. the value of \(d\),
  2. the value of \(M\).
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Edexcel M1 2016 June Q7
11 marks Moderate -0.3
7. Two forces \(\mathbf { F } _ { 1 }\) and \(\mathbf { F } _ { 2 }\) act on a particle \(P\). The force \(\mathbf { F } _ { 1 }\) is given by \(\mathbf { F } _ { 1 } = ( - \mathbf { i } + 2 \mathbf { j } ) \mathrm { N }\) and \(\mathbf { F } _ { 2 }\) acts in the direction of the vector \(( \mathbf { i } + \mathbf { j } )\).
Given that the resultant of \(\mathbf { F } _ { 1 }\) and \(\mathbf { F } _ { 2 }\) acts in the direction of the vector ( \(\mathbf { i } + 3 \mathbf { j }\) ),
  1. find \(\mathbf { F } _ { 2 }\)
    (7) The acceleration of \(P\) is \(( 3 \mathbf { i } + 9 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }\). At time \(t = 0\), the velocity of \(P\) is \(( 3 \mathbf { i } - 22 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\)
  2. Find the speed of \(P\) when \(t = 3\) seconds.
Edexcel M1 2016 June Q8
12 marks Standard +0.3
8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d408dd83-c5b2-4e55-b5c1-3e7f3faadbcb-14_460_981_274_475} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Two particles \(P\) and \(Q\) have masses 1.5 kg and 3 kg respectively. The particles are attached to the ends of a light inextensible string. Particle \(P\) is held at rest on a fixed rough horizontal table. The coefficient of friction between \(P\) and the table is \(\frac { 1 } { 5 }\). The string is parallel to the table and passes over a small smooth light pulley which is fixed at the edge of the table. Particle \(Q\) hangs freely at rest vertically below the pulley, as shown in Figure 3. Particle \(P\) is released from rest with the string taut and slides along the table. Assuming that \(P\) has not reached the pulley, find
  1. the tension in the string during the motion,
  2. the magnitude and direction of the resultant force exerted on the pulley by the string.
Edexcel M1 2017 June Q1
6 marks Moderate -0.8
  1. Three forces, \(( 15 \mathbf { i } + \mathbf { j } ) \mathrm { N } , ( 5 q \mathbf { i } - p \mathbf { j } ) \mathrm { N }\) and \(( - 3 p \mathbf { i } - q \mathbf { j } ) \mathrm { N }\), where \(p\) and \(q\) are constants, act on a particle. Given that the particle is in equilibrium, find the value of \(p\) and the value of \(q\).
    (6)
Edexcel M1 2017 June Q2
7 marks Moderate -0.8
2. Two particles, \(P\) and \(Q\), have masses \(2 m\) and \(3 m\) respectively. They are moving towards each other in opposite directions on a smooth horizontal plane when they collide directly. Immediately before they collide the speed of \(P\) is \(4 u\) and the speed of \(Q\) is \(3 u\). As a result of the collision, \(Q\) has its direction of motion reversed and is moving with speed \(u\).
  1. Find the speed of \(P\) immediately after the collision.
  2. State whether or not the direction of motion of \(P\) has been reversed by the collision.
  3. Find the magnitude of the impulse exerted on \(P\) by \(Q\) in the collision.
Edexcel M1 2017 June Q3
9 marks Standard +0.3
3. A plank \(A B\) has length 6 m and mass 30 kg . The point \(C\) is on the plank with \(C B = 2 \mathrm {~m}\). The plank rests in equilibrium in a horizontal position on supports at \(A\) and \(C\). Two people, each of mass 75 kg , stand on the plank. One person stands at the point \(P\) of the plank, where \(A P = x\) metres, and the other person stands at the point \(Q\) of the plank, where \(A Q = 2 x\) metres. The plank remains horizontal and in equilibrium with the magnitude of the reaction at \(C\) five times the magnitude of the reaction at \(A\). The plank is modelled as a uniform rod and each person is modelled as a particle.
  1. Find the value of \(x\).
  2. State two ways in which you have used the assumptions made in modelling the plank as a uniform rod.