Questions — Edexcel M1 (599 questions)

Browse by module
All questions AEA AS Paper 1 AS Paper 2 AS Pure 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 Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Extra Pure Further Mechanics Further Mechanics A AS Further Mechanics AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics Further Paper 4 Further Pure Core Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Pure with Technology Further Statistics Further Statistics A AS Further Statistics AS Further Statistics B AS Further Statistics Major Further Statistics Minor Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 H240/01 H240/02 H240/03 M1 M2 M3 M4 M5 Mechanics 1 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 Pure 1 S1 S2 S3 S4 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 Stats 1 Unit 1 Unit 2 Unit 3 Unit 4
Browse by board
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 2010 January Q1
  1. A particle \(A\) of mass 2 kg is moving along a straight horizontal line with speed \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Another particle \(B\) of mass \(m \mathrm {~kg}\) is moving along the same straight line, in the opposite direction to \(A\), with speed \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The particles collide. The direction of motion of \(A\) is unchanged by the collision. Immediately after the collision, \(A\) is moving with speed \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(B\) is moving with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find
    1. the magnitude of the impulse exerted by \(B\) on \(A\) in the collision,
    2. the value of \(m\).
    3. An athlete runs along a straight road. She starts from rest and moves with constant acceleration for 5 seconds, reaching a speed of \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). This speed is then maintained for \(T\) seconds. She then decelerates at a constant rate until she stops. She has run a total of 500 m in 75 s .
    4. In the space below, sketch a speed-time graph to illustrate the motion of the athlete.
    5. Calculate the value of \(T\).
    \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{330c2068-fe0a-4c6d-b892-79ab173c6a11-04_271_750_214_598} \captionsetup{labelformat=empty} \caption{Figure 1}
    \end{figure} A particle of mass \(m \mathrm {~kg}\) is attached at \(C\) to two light inextensible strings \(A C\) and \(B C\). The other ends of the strings are attached to fixed points \(A\) and \(B\) on a horizontal ceiling. The particle hangs in equilibrium with \(A C\) and \(B C\) inclined to the horizontal at \(30 ^ { \circ }\) and \(60 ^ { \circ }\) respectively, as shown in Figure 1. Given that the tension in \(A C\) is 20 N , find
  2. the tension in \(B C\),
  3. the value of \(m\).
Edexcel M1 2010 January Q4
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{330c2068-fe0a-4c6d-b892-79ab173c6a11-05_557_673_127_646} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A pole \(A B\) has length 3 m and weight \(W\) newtons. The pole is held in a horizontal position in equilibrium by two vertical ropes attached to the pole at the points \(A\) and \(C\) where \(A C = 1.8 \mathrm {~m}\), as shown in Figure 2. A load of weight 20 N is attached to the rod at \(B\). The pole is modelled as a uniform rod, the ropes as light inextensible strings and the load as a particle.
  1. Show that the tension in the rope attached to the pole at \(C\) is \(\left( \frac { 5 } { 6 } W + \frac { 100 } { 3 } \right) \mathrm { N }\).
  2. Find, in terms of \(W\), the tension in the rope attached to the pole at \(A\). Given that the tension in the rope attached to the pole at \(C\) is eight times the tension in the rope attached to the pole at \(A\),
  3. find the value of \(W\).
Edexcel M1 2010 January Q5
  1. A particle of mass 0.8 kg is held at rest on a rough plane. The plane is inclined at \(30 ^ { \circ }\) to the horizontal. The particle is released from rest and slides down a line of greatest slope of the plane. The particle moves 2.7 m during the first 3 seconds of its motion. Find
    1. the acceleration of the particle,
    2. the coefficient of friction between the particle and the plane.
    The particle is now held on the same rough plane by a horizontal force of magnitude \(X\) newtons, acting in a plane containing a line of greatest slope of the plane, as shown in Figure 3. The particle is in equilibrium and on the point of moving up the plane. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{330c2068-fe0a-4c6d-b892-79ab173c6a11-07_255_725_890_621} \captionsetup{labelformat=empty} \caption{Figure 3}
    \end{figure}
  2. Find the value of \(X\).
Edexcel M1 2010 January Q6
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{330c2068-fe0a-4c6d-b892-79ab173c6a11-09_519_537_210_708} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Two particles \(A\) and \(B\) have masses \(5 m\) and \(k m\) respectively, where \(k < 5\). The particles 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, the hanging parts of the string vertical and with \(A\) and \(B\) at the same height above a horizontal plane, as shown in Figure 4. The system is released from rest. After release, \(A\) descends with acceleration \(\frac { 1 } { 4 } g\).
  1. Show that the tension in the string as \(A\) descends is \(\frac { 15 } { 4 } \mathrm { mg }\).
  2. Find the value of \(k\).
  3. State how you have used the information that the pulley is smooth. After descending for 1.2 s , the particle \(A\) reaches the plane. It is immediately brought to rest by the impact with the plane. The initial distance between \(B\) and the pulley is such that, in the subsequent motion, \(B\) does not reach the pulley.
  4. Find the greatest height reached by \(B\) above the plane.
Edexcel M1 2010 January Q7
7. [In this question, \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors due east and due north respectively and position vectors are given with respect to a fixed origin.] A ship \(S\) is moving along a straight line with constant velocity. At time \(t\) hours the position vector of \(S\) is \(\mathbf { s } \mathrm { km }\). When \(t = 0 , \mathbf { s } = 9 \mathbf { i } - 6 \mathbf { j }\). When \(t = 4 , \mathbf { s } = 21 \mathbf { i } + 10 \mathbf { j }\). Find
  1. the speed of \(S\),
  2. the direction in which \(S\) is moving, giving your answer as a bearing.
  3. Show that \(\mathbf { s } = ( 3 t + 9 ) \mathbf { i } + ( 4 t - 6 ) \mathbf { j }\). A lighthouse \(L\) is located at the point with position vector \(( 18 \mathbf { i } + 6 \mathbf { j } ) \mathrm { km }\). When \(t = T\), the ship \(S\) is 10 km from \(L\).
  4. Find the possible values of \(T\).
Edexcel M1 2011 January Q1
  1. Two particles \(B\) and \(C\) have mass \(m \mathrm {~kg}\) and 3 kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table. The two particles collide directly. Immediately before the collision, the speed of \(B\) is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(C\) is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). In the collision the direction of motion of \(C\) is reversed and the direction of motion of \(B\) is unchanged. Immediately after the collision, the speed of \(B\) is \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(C\) is \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Find
  1. the value of \(m\),
  2. the magnitude of the impulse received by \(C\).
Edexcel M1 2011 January Q2
2. A ball is thrown vertically upwards with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point \(P\) at height \(h\) metres above the ground. The ball hits the ground 0.75 s later. The speed of the ball immediately before it hits the ground is \(6.45 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The ball is modelled as a particle.
  1. Show that \(u = 0.9\)
  2. Find the height above \(P\) to which the ball rises before it starts to fall towards the ground again.
  3. Find the value of \(h\).
Edexcel M1 2011 January Q3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4878b6c2-0c62-4398-8a8f-913139bc8a14-04_245_860_260_543} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A uniform beam \(A B\) has mass 20 kg and length 6 m . The beam rests in equilibrium in a horizontal position on two smooth supports. One support is at \(C\), where \(A C = 1 \mathrm {~m}\), and the other is at the end \(B\), as shown in Figure 1. The beam is modelled as a rod.
  1. Find the magnitudes of the reactions on the beam at \(B\) and at \(C\). A boy of mass 30 kg stands on the beam at the point \(D\). The beam remains in equilibrium. The magnitudes of the reactions on the beam at \(B\) and at \(C\) are now equal. The boy is modelled as a particle.
  2. Find the distance \(A D\).
Edexcel M1 2011 January Q4
  1. A particle \(P\) of mass 2 kg is moving under the action of a constant force \(\mathbf { F }\) newtons. The velocity of \(P\) is \(( 2 \mathbf { i } - 5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) at time \(t = 0\), and \(( 7 \mathbf { i } + 10 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) at time \(t = 5 \mathrm {~s}\).
Find
  1. the speed of \(P\) at \(t = 0\),
  2. the vector \(\mathbf { F }\) in the form \(a \mathbf { i } + b \mathbf { j }\),
  3. the value of \(t\) when \(P\) is moving parallel to \(\mathbf { i }\).
Edexcel M1 2011 January Q5
  1. A car accelerates uniformly from rest for 20 seconds. It moves at constant speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for the next 40 seconds and then decelerates uniformly for 10 seconds until it comes to rest.
    1. For the motion of the car, sketch
      1. a speed-time graph,
      2. an acceleration-time graph.
    Given that the total distance moved by the car is 880 m ,
  2. find the value of \(v\).
Edexcel M1 2011 January Q6
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4878b6c2-0c62-4398-8a8f-913139bc8a14-10_426_768_239_653} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A particle of weight 120 N is placed on a fixed rough plane which is inclined at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 3 } { 4 }\).
The coefficient of friction between the particle and the plane is \(\frac { 1 } { 2 }\).
The particle is held at rest in equilibrium by a horizontal force of magnitude 30 N , which acts in the vertical plane containing the line of greatest slope of the plane through the particle, as shown in Figure 2.
  1. Show that the normal reaction between the particle and the plane has magnitude 114 N . \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{4878b6c2-0c62-4398-8a8f-913139bc8a14-10_433_774_1464_604} \captionsetup{labelformat=empty} \caption{Figure 3}
    \end{figure} The horizontal force is removed and replaced by a force of magnitude \(P\) newtons acting up the slope along the line of greatest slope of the plane through the particle, as shown in Figure 3. The particle remains in equilibrium.
  2. Find the greatest possible value of \(P\).
  3. Find the magnitude and direction of the frictional force acting on the particle when \(P = 30\).
Edexcel M1 2011 January Q7
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4878b6c2-0c62-4398-8a8f-913139bc8a14-12_581_1211_235_370} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Two particles \(A\) and \(B\), of mass 7 kg and 3 kg respectively, are attached to the ends of a light inextensible string. Initially \(B\) is held at rest on a rough fixed plane inclined at angle \(\theta\) to the horizontal, where \(\tan \theta = \frac { 5 } { 12 }\). The part of the string from \(B\) to \(P\) is parallel to a line of greatest slope of the plane. The string passes over a small smooth pulley, \(P\), fixed at the top of the plane. The particle \(A\) hangs freely below \(P\), as shown in Figure 4. The coefficient of friction between \(B\) and the plane is \(\frac { 2 } { 3 }\). The particles are released from rest with the string taut and \(B\) moves up the plane.
  1. Find the magnitude of the acceleration of \(B\) immediately after release.
  2. Find the speed of \(B\) when it has moved 1 m up the plane. When \(B\) has moved 1 m up the plane the string breaks. Given that in the subsequent motion \(B\) does not reach \(P\),
  3. find the time between the instants when the string breaks and when \(B\) comes to instantaneous rest.
Edexcel M1 2012 January Q1
  1. A railway truck \(P\), of mass \(m \mathrm {~kg}\), is moving along a straight horizontal track with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Truck \(P\) collides with a truck \(Q\) of mass 3000 kg , which is at rest on the same track. Immediately after the collision the speed of \(P\) is \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(Q\) is \(9 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The direction of motion of \(P\) is reversed by the collision.
Modelling the trucks as particles, find
  1. the magnitude of the impulse exerted by \(P\) on \(Q\),
  2. the value of \(m\).
Edexcel M1 2012 January Q2
2. A car of mass 1000 kg is towing a caravan of mass 750 kg along a straight horizontal road. The caravan is connected to the car by a tow-bar which is parallel to the direction of motion of the car and the caravan. The tow-bar is modelled as a light rod. The engine of the car provides a constant driving force of 3200 N . The resistances to the motion of the car and the caravan are modelled as constant forces of magnitude 800 newtons and \(R\) newtons respectively. Given that the acceleration of the car and the caravan is \(0.88 \mathrm {~ms} ^ { - 2 }\),
  1. show that \(R = 860\),
  2. find the tension in the tow-bar.
Edexcel M1 2012 January Q3
3. Three forces \(\mathbf { F } _ { 1 } , \mathbf { F } _ { 2 }\) and \(\mathbf { F } _ { 3 }\) acting on a particle \(P\) are given by $$\begin{aligned} & \mathbf { F } _ { 1 } = ( 7 \mathbf { i } - 9 \mathbf { j } ) \mathrm { N }
& \mathbf { F } _ { 2 } = ( 5 \mathbf { i } + 6 \mathbf { j } ) \mathrm { N }
& \mathbf { F } _ { 3 } = ( p \mathbf { i } + q \mathbf { j } ) \mathrm { N } \end{aligned}$$ where \(p\) and \(q\) are constants.
Given that \(P\) is in equilibrium,
  1. find the value of \(p\) and the value of \(q\). The force \(\mathbf { F } _ { 3 }\) is now removed. The resultant of \(\mathbf { F } _ { 1 }\) and \(\mathbf { F } _ { 2 }\) is \(\mathbf { R }\). Find
  2. the magnitude of \(\mathbf { R }\),
  3. the angle, to the nearest degree, that the direction of \(\mathbf { R }\) makes with \(\mathbf { j }\).
Edexcel M1 2012 January Q4
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{724254f3-3a6a-4820-b3a1-979458e24437-05_241_794_219_575} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A non-uniform \(\operatorname { rod } A B\), of mass \(m\) and length \(5 d\), rests horizontally in equilibrium on two supports at \(C\) and \(D\), where \(A C = D B = d\), as shown in Figure 1. The centre of mass of the rod is at the point \(G\). A particle of mass \(\frac { 5 } { 2 } m\) is placed on the rod at \(B\) and the rod is on the point of tipping about \(D\).
  1. Show that \(G D = \frac { 5 } { 2 } d\). The particle is moved from \(B\) to the mid-point of the rod and the rod remains in equilibrium.
  2. Find the magnitude of the normal reaction between the support at \(D\) and the rod.
Edexcel M1 2012 January Q5
  1. A stone is projected vertically upwards from a point \(A\) with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\). After projection the stone moves freely under gravity until it returns to \(A\). The time between the instant that the stone is projected and the instant that it returns to \(A\) is \(3 \frac { 4 } { 7 }\) seconds.
Modelling the stone as a particle,
  1. show that \(u = 17 \frac { 1 } { 2 }\),
  2. find the greatest height above \(A\) reached by the stone,
  3. find the length of time for which the stone is at least \(6 \frac { 3 } { 5 } \mathrm {~m}\) above \(A\).
Edexcel M1 2012 January Q6
  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.
Edexcel M1 2012 January Q7
7. [In this question, the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are due east and due north respectively. Position vectors are relative to a fixed origin \(O\).] A boat \(P\) is moving with constant velocity \(( - 4 \mathbf { i } + 8 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\).
  1. Calculate the speed of \(P\). When \(t = 0\), the boat \(P\) has position vector \(( 2 \mathbf { i } - 8 \mathbf { j } ) \mathrm { km }\). At time \(t\) hours, the position vector of \(P\) is \(\mathbf { p ~ k m }\).
  2. Write down \(\mathbf { p }\) in terms of \(t\). A second boat \(Q\) is also moving with constant velocity. At time \(t\) hours, the position vector of \(Q\) is \(\mathbf { q } \mathrm { km }\), where $$\mathbf { q } = 18 \mathbf { i } + 12 \mathbf { j } - t ( 6 \mathbf { i } + 8 \mathbf { j } )$$ Find
  3. the value of \(t\) when \(P\) is due west of \(Q\),
  4. the distance between \(P\) and \(Q\) when \(P\) is due west of \(Q\).
Edexcel M1 2012 January Q8
8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{724254f3-3a6a-4820-b3a1-979458e24437-13_334_538_219_703} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A particle \(P\) of mass 4 kg is moving up a fixed rough plane at a constant speed of \(16 \mathrm {~ms} ^ { - 1 }\) under the action of a force of magnitude 36 N . The plane is inclined at \(30 ^ { \circ }\) to the horizontal. The force acts in the vertical plane containing the line of greatest slope of the plane through \(P\), and acts at \(30 ^ { \circ }\) to the inclined plane, as shown in Figure 2. The coefficient of friction between \(P\) and the plane is \(\mu\). Find
  1. the magnitude of the normal reaction between \(P\) and the plane,
  2. the value of \(\mu\). The force of magnitude 36 N is removed.
  3. Find the distance that \(P\) travels between the instant when the force is removed and the instant when it comes to rest.
Edexcel M1 2001 June Q1
  1. Two small balls \(A\) and \(B\) have masses 0.5 kg and 0.2 kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of \(A\) is \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the speed of \(B\) is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The speed of \(A\) immediately after the collision is \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The direction of the motion of \(A\) is unchanged as a result of the collision.
By modelling the balls as particles, find
  1. the speed of \(B\) immediately after the collision,
  2. the magnitude of the impulse exerted on \(B\) in the collision.
Edexcel M1 2001 June Q2
2. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{218383c1-0875-46f2-9416-8e827065a7a6-2_272_592_1239_648}
\end{figure} Two forces \(\mathbf { P }\) and \(\mathbf { Q }\), act on a particle. The force \(\mathbf { P }\) has magnitude 5 N and the force \(\mathbf { Q }\) has magnitude 3 N . The angle between the directions of \(\mathbf { P }\) and \(\mathbf { Q }\) is \(40 ^ { \circ }\), as shown in Fig. 1. The resultant of \(\mathbf { P }\) and \(\mathbf { Q }\) is \(\mathbf { F }\).
  1. Find, to 3 significant figures, the magnitude of \(\mathbf { F }\).
  2. Find, in degrees to 1 decimal place, the angle between the directions of \(\mathbf { F }\) and \(\mathbf { P }\).
Edexcel M1 2001 June Q3
3. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{218383c1-0875-46f2-9416-8e827065a7a6-3_540_1223_348_455}
\end{figure} A car of mass 1200 kg moves along a straight horizontal road. In order to obey a speed restriction, the brakes of the car are applied for 3 s , reducing the car's speed from \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) to \(17 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The brakes are then released and the car continues at a constant speed of \(17 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for a further 4 s . Figure 2 shows a sketch of the speed-time graph of the car during the 7 s interval. The graph consists of two straight line segments.
  1. Find the total distance moved by the car during this 7 s interval.
  2. Explain briefly how the speed-time graph shows that, when the brakes are applied, the car experiences a constant retarding force.
  3. Find the magnitude of this retarding force.
Edexcel M1 2001 June Q4
4. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 3} \includegraphics[alt={},max width=\textwidth]{218383c1-0875-46f2-9416-8e827065a7a6-4_347_854_356_640}
\end{figure} A small parcel of mass 3 kg is held in equilibrium on a rough plane by the action of a horizontal force of magnitude 30 N acting in a vertical plane through a line of greatest slope. The plane is inclined at an angle of \(30 ^ { \circ }\) to the horizontal, as shown in Fig. 3. The parcel is modelled as a particle. The parcel is on the point of moving up the slope.
  1. Draw a diagram showing all the forces acting on the parcel.
  2. Find the normal reaction on the parcel.
  3. Find the coefficient of friction between the parcel and the plane.
Edexcel M1 2001 June Q5
5. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 4} \includegraphics[alt={},max width=\textwidth]{218383c1-0875-46f2-9416-8e827065a7a6-5_328_993_491_483}
\end{figure} A large \(\log A B\) is 6 m long. It rests in a horizontal position on two smooth supports \(C\) and \(D\), where \(A C = 1 \mathrm {~m}\) and \(B D = 1 \mathrm {~m}\), as shown in Figure 4. David needs an estimate of the weight of the log, but the log is too heavy to lift off both supports. When David applies a force of magnitude 1500 N vertically upwards to the \(\log\) at \(A\), the \(\log\) is about to tilt about \(D\).
  1. State the value of the reaction on the \(\log\) at \(C\) for this case. David initially models the log as uniform rod. Using this model,
  2. estimate the weight of the log The shape of the log convinces David that his initial modelling assumption is too simple. He removes the force at \(A\) and applies a force acting vertically upwards at \(B\). He finds that the log is about to tilt about \(C\) when this force has magnitude 1000 N. David now models the log as a non-uniform rod, with the distance of the centre of mass of the \(\log\) from \(C\) as \(x\) metres. Using this model, find
  3. a new estimate for the weight of the log,
  4. the value of \(x\).
  5. State how you have used the modeling assumption that the log is a rod.