Questions M1 (1912 questions)

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Edexcel M1 2015 January Q5
10 marks Standard +0.8
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{aaa8b297-347c-4a9b-a2c2-c4bd70d56912-07_237_657_264_703} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A particle \(P\) of mass 2 kg is pushed up a line of greatest slope of a rough plane by a horizontal force of magnitude \(X\) newtons, as shown in Figure 2. The force acts in the vertical plane which contains \(P\) and a line of greatest slope of the plane. The plane is inclined to the horizontal at an angle \(\alpha\), where \(\tan \alpha = \frac { 3 } { 4 }\)
The coefficient of friction between \(P\) and the plane is 0.5
Given that the acceleration of \(P\) is \(1.45 \mathrm {~m} \mathrm {~s} ^ { - 2 }\), find the value of \(X\).
Edexcel M1 2015 January Q6
10 marks Standard +0.3
6. A uniform rod \(A C\), of weight \(W\) and length \(3 l\), rests horizontally on two supports, one at \(A\) and one at \(B\), where \(A B = 2 l\). A particle of weight \(2 W\) is placed on the rod at a distance \(x\) from \(A\). The rod remains horizontal and in equilibrium.
  1. Find the greatest possible value of \(x\). The magnitude of the reaction of the support at \(A\) is \(R\). Due to a weakness in the support at \(A\), the greatest possible value of \(R\) is \(2 W\),
  2. find the least possible value of \(x\).
Edexcel M1 2015 January Q7
10 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 until it reaches its maximum speed of \(108 \mathrm {~km} \mathrm {~h} ^ { - 1 }\). The train then travels at this speed before it moves with constant deceleration coming to rest at \(B\). The journey from \(A\) to \(B\) takes 8 minutes.
  1. Change \(108 \mathrm {~km} \mathrm {~h} ^ { - 1 }\) into \(\mathrm { m } \mathrm { s } ^ { - 1 }\).
  2. Sketch a speed-time graph for the motion of the train between the two stations \(A\) and \(B\). Given that the distance between the two stations is 12 km and that the time spent decelerating is three times the time spent accelerating,
  3. find the acceleration, in \(\mathrm { m } \mathrm { s } ^ { - 2 }\), of the train.
Edexcel M1 2015 January Q8
16 marks Standard +0.3
8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{aaa8b297-347c-4a9b-a2c2-c4bd70d56912-13_668_901_262_566} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A particle \(A\) of mass \(3 m\) is held at rest on a rough horizontal table. The particle is attached to one end of a light inextensible string. The string passes over a small smooth pulley \(P\) which is fixed at the edge of the table. The other end of the string is attached to a particle \(B\) of mass \(2 m\), which hangs freely, vertically below \(P\). The system is released from rest, with the string taut, when \(A\) is 1.3 m from \(P\) and \(B\) is 1 m above the horizontal floor, as shown in Figure 3. Given that \(B\) hits the floor 2 s after release and does not rebound,
  1. find the acceleration of \(A\) during the first two seconds,
  2. find the coefficient of friction between \(A\) and the table,
  3. determine whether \(A\) reaches the pulley.
    \includegraphics[max width=\textwidth, alt={}, center]{aaa8b297-347c-4a9b-a2c2-c4bd70d56912-14_106_59_2478_1833}
Edexcel M1 2016 January Q1
7 marks Moderate -0.8
  1. A truck of mass 2400 kg is pulling a trailer of mass \(M \mathrm {~kg}\) along a straight horizontal road. The tow bar, connecting the truck to the trailer, is horizontal and parallel to the direction of motion. The tow bar is modelled as being light and inextensible. The resistance forces acting on the truck and the trailer are constant and of magnitude 400 N and 200 N respectively. The acceleration of the truck is \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) and the tension in the tow bar is 600 N.
    1. Find the magnitude of the driving force of the truck.
    2. Find the value of \(M\).
    3. Explain how you have used the fact that the tow bar is inextensible in your calculations.
Edexcel M1 2016 January Q2
8 marks Moderate -0.5
  1. Two particles \(P\) and \(Q\) are moving in opposite directions along the same horizontal straight line. Particle \(P\) is moving due east and particle \(Q\) is moving due west. Particle \(P\) has mass \(2 m\) and particle \(Q\) has mass \(3 m\). The particles collide directly. Immediately before the collision, the speed of \(P\) is \(4 u\) and the speed of \(Q\) is \(u\). The magnitude of the impulse in the collision is \(\frac { 33 } { 5 } m u\).
    1. Find the speed and direction of motion of \(P\) immediately after the collision.
    2. Find the speed and direction of motion of \(Q\) immediately after the collision.
      VILIV SIMI NI III IM I ON OC
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      VALV SIHI NI JIIUM ION OC
    \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{054e11cb-9416-40c0-9dde-8d12818bab3f-04_268_862_123_543} \captionsetup{labelformat=empty} \caption{Figure 1}
    \end{figure} A boy is pulling a sledge of mass 8 kg in a straight line at a constant speed across rough horizontal ground by means of a rope. The rope is inclined at \(30 ^ { \circ }\) to the ground, as shown in Figure 1. The coefficient of friction between the sledge and the ground is \(\frac { 1 } { 5 }\). By modelling the sledge as a particle and the rope as a light inextensible string, find the tension in the rope.
Edexcel M1 2016 January Q4
13 marks Moderate -0.8
4. A small stone is projected vertically upwards from the point \(O\) and moves freely under gravity. The point \(A\) is 3.6 m vertically above \(O\). When the stone first reaches \(A\), the stone is moving upwards with speed \(11.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The stone is modelled as a particle.
  1. Find the maximum height above \(O\) reached by the stone.
  2. Find the total time between the instant when the stone was projected from \(O\) and the instant when it returns to \(O\).
  3. Sketch a velocity-time graph to represent the motion of the stone from the instant when it passes through \(A\) moving upwards to the instant when it returns to \(O\). Show, on the axes, the coordinates of the points where your graph meets the axes.
Edexcel M1 2016 January Q5
10 marks Standard +0.3
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{054e11cb-9416-40c0-9dde-8d12818bab3f-07_531_1182_114_383} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A non-uniform rod \(A B\) has length 4 m and weight 120 N . The centre of mass of the rod is at the point \(G\) where \(A G = 2.2 \mathrm {~m}\). The rod is suspended in a horizontal position by two vertical light inextensible strings, one at each end, as shown in Figure 2. A particle of weight 40 N is placed on the rod at the point \(P\), where \(A P = x\) metres. The rod remains horizontal and in equilibrium.
  1. Find, in terms of \(x\),
    1. the tension in the string at \(A\),
    2. the tension in the string at \(B\). Either string will break if the tension in it exceeds 84 N .
  2. Find the range of possible values of \(x\).
Edexcel M1 2016 January Q6
13 marks Moderate -0.3
6. [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.] At 2 pm , the position vector of ship \(P\) is \(( 5 \mathbf { i } - 3 \mathbf { j } ) \mathrm { km }\) and the position vector of ship \(Q\) is \(( 7 \mathbf { i } + 5 \mathbf { j } ) \mathrm { km }\).
  1. Find the distance between \(P\) and \(Q\) at 2 pm . Ship \(P\) is moving with constant velocity \(( 2 \mathbf { i } + 5 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\) and ship \(Q\) is moving with constant velocity \(( - 3 \mathbf { i } - 15 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\).
  2. Find the position vector of \(P\) at time \(t\) hours after 2 pm .
  3. Find the position vector of \(Q\) at time \(t\) hours after 2 pm .
  4. Show that \(Q\) will meet \(P\) and find the time at which they meet.
  5. Find the position vector of the point at which they meet.
Edexcel M1 2016 January Q7
16 marks Standard +0.3
7. $$P ( 2 \mathrm {~kg} )$$ \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{054e11cb-9416-40c0-9dde-8d12818bab3f-11_529_899_269_525} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A particle \(P\) of mass 2 kg is attached to one end of a light inextensible string. A particle \(Q\) of mass 5 kg is attached to the other end of the string. The string passes over a small smooth light pulley. The pulley is fixed at a point on the intersection of a rough horizontal table and a fixed smooth inclined plane. The string lies along the table and also lies in a vertical plane which contains a line of greatest slope of the inclined plane. This plane is inclined to the horizontal at an angle \(\alpha\), where \(\tan \alpha = \frac { 3 } { 4 }\). Particle \(P\) is at rest on the table, a distance \(d\) metres from the pulley. Particle \(Q\) is on the inclined plane with the string taut, as shown in Figure 3. The coefficient of friction between \(P\) and the table is \(\frac { 1 } { 4 }\). The system is released from rest and \(P\) slides along the table towards the pulley.
Assuming that \(P\) has not reached the pulley and that \(Q\) remains on the inclined plane,
  1. write down an equation of motion for \(P\),
  2. write down an equation of motion for \(Q\),
    1. find the acceleration of \(P\),
    2. find the tension in the string. When \(P\) has moved a distance 0.5 m from its initial position, the string breaks. Given that \(P\) comes to rest just as it reaches the pulley,
  4. find the value of \(d\).
Edexcel M1 2017 January Q1
9 marks Easy -1.2
  1. A train moves along a straight horizontal track between two stations \(R\) and \(S\). Initially the train is at rest at \(R\). The train accelerates uniformly at \(\frac { 1 } { 2 } \mathrm {~m} \mathrm {~s} ^ { - 2 }\) from rest at \(R\) until it is moving with speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). For the next 200 seconds the train maintains a constant speed of \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The train then decelerates uniformly at \(\frac { 1 } { 4 } \mathrm {~m} \mathrm {~s} ^ { - 2 }\) until it comes to rest at \(S\).
Find
  1. the time taken by the train to travel from \(R\) to \(S\),
  2. the distance from \(R\) to \(S\),
  3. the average speed of the train during the journey from \(R\) to \(S\).
Edexcel M1 2017 January Q2
9 marks Moderate -0.8
  1. A particle \(P\) of mass 0.5 kg moves under the action of a single constant force ( \(2 \mathbf { i } + 3 \mathbf { j }\) )N.
    1. Find the acceleration of \(P\).
    At time \(t\) seconds, \(P\) has velocity \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\). When \(t = 0 , \mathbf { v } = 4 \mathbf { i }\)
  2. Find the speed of \(P\) when \(t = 3\) Given that \(P\) is moving parallel to the vector \(2 \mathbf { i } + \mathbf { j }\) at time \(t = T\)
  3. find the value of \(T\).
Edexcel M1 2017 January Q3
8 marks Moderate -0.8
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-05_520_730_264_607} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Two forces \(\mathbf { P }\) and \(\mathbf { Q }\) act on a particle at a point \(O\). Force \(\mathbf { P }\) has magnitude 6 N and force \(\mathbf { Q }\) has magnitude 7 N . The angle between the line of action of \(\mathbf { P }\) and the line of action of \(\mathbf { Q }\) is \(120 ^ { \circ }\), as shown in Figure 1. The resultant of \(\mathbf { P }\) and \(\mathbf { Q }\) is \(\mathbf { R }\). Find
  1. the magnitude of \(\mathbf { R }\),
  2. the angle between the line of action of \(\mathbf { R }\) and the line of action of \(\mathbf { P }\).
Edexcel M1 2017 January Q4
13 marks Moderate -0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-06_266_1440_239_251} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A plank \(A B\) of mass 20 kg and length 8 m is resting in a horizontal position on two supports at \(C\) and \(D\), where \(A C = 1.5 \mathrm {~m}\) and \(D B = 2 \mathrm {~m}\). A package of mass 8 kg is placed on the plank at \(C\), as shown in Figure 2. The plank remains horizontal and in equilibrium. The plank is modelled as a uniform rod and the package is modelled as a particle.
  1. Find the magnitude of the normal reaction
    1. between the plank and the support at \(C\),
    2. between the plank and the support at \(D\).
      (6) The package is now moved along the plank to the point \(E\). When the package is at \(E\), the magnitude of the normal reaction between the plank and the support at \(C\) is \(R\) newtons and the magnitude of the normal reaction between the plank and the support at \(D\) is \(2 R\) newtons.
  2. Find the distance \(A E\).
  3. State how you have used the fact that the package is modelled as a particle.
Edexcel M1 2017 January Q5
8 marks Standard +0.3
  1. Two particles \(P\) and \(Q\) have masses \(4 m\) and \(k m\) respectively. They are moving towards each other in opposite directions along the same straight line on a smooth horizontal table when they collide directly. Immediately before the collision the speed of \(P\) is \(3 u\) and the speed of \(Q\) is \(u\). Immediately after the collision both particles have speed \(2 u\) and the direction of motion of \(Q\) has been reversed.
    1. Find, in terms of \(k , m\) and \(u\), the magnitude of the impulse received by \(Q\) in the collision.
    2. Find the two possible values of \(k\).
Edexcel M1 2017 January Q6
14 marks Standard +0.3
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-10_609_1013_118_456} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A particle \(P\) of mass 4 kg is held at rest at the point \(A\) on a rough plane which is inclined at \(30 ^ { \circ }\) to the horizontal. The point \(B\) lies on the line of greatest slope of the plane that passes through \(A\). The point \(B\) is 5 m down the plane from \(A\), as shown in Figure 3. The coefficient of friction between the plane and \(P\) is 0.3 The particle is released from rest at \(A\) and slides down the plane.
  1. Find the speed of \(P\) at the instant it reaches \(B\). \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-10_478_1011_1343_456} \captionsetup{labelformat=empty} \caption{Figure 4}
    \end{figure} The particle is now returned to \(A\) and is held in equilibrium by a horizontal force of magnitude \(H\) newtons, as shown in Figure 4. The line of action of the force lies in the vertical plane containing the line of greatest slope of the plane through \(A\). The particle is on the point of moving up the plane.
  2. Find the value of \(H\).
Edexcel M1 2017 January Q7
14 marks Standard +0.3
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba698f74-a51c-409a-a9d9-e9080fc87be2-12_524_586_274_696} \captionsetup{labelformat=empty} \caption{Figure 5}
\end{figure} Two particles \(P\) and \(Q\) have masses 3 kg and \(m \mathrm {~kg}\) respectively ( \(m > 3\) ). 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 and the hanging parts of the string vertical. The particle \(Q\) is at a height of 10.5 m above the horizontal ground, as shown in Figure 5. The system is released from rest and \(Q\) moves downwards. In the subsequent motion \(P\) does not reach the pulley. After the system is released, the tension in the string is 33.6 N .
  1. Show that the magnitude of the acceleration of \(P\) is \(1.4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
  2. Find the value of \(m\). The system is released from rest at time \(t = 0\). At time \(T _ { 1 }\) seconds after release, \(Q\) strikes the ground and does not rebound. The string goes slack and \(P\) continues to move upwards.
  3. Find the value of \(T _ { 1 }\) At time \(T _ { 2 }\) seconds after release, \(P\) comes to instantaneous rest.
  4. Find the value of \(T _ { 2 }\) At time \(T _ { 3 }\) seconds after release ( \(T _ { 3 } > T _ { 1 }\) ) the string becomes taut again.
  5. Sketch a velocity-time graph for the motion of \(P\) in the interval \(0 \leqslant t \leqslant T _ { 3 }\)
Edexcel M1 2018 January Q1
7 marks Moderate -0.8
1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{04b73f81-3316-4f26-ad98-a7be3a4b738f-02_297_812_240_567} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A particle of weight \(W\) 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 the strings in a vertical plane and with \(A C\) and \(B C\) inclined to the horizontal at \(30 ^ { \circ }\) and \(45 ^ { \circ }\) respectively, as shown in Figure 1. Find, in terms of \(W\),
  1. the tension in \(A C\),
  2. the tension in \(B C\).
    VILLI SIHI NITIIIUM ION OC
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Edexcel M1 2018 January Q2
6 marks Standard +0.3
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{04b73f81-3316-4f26-ad98-a7be3a4b738f-06_241_768_214_589} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A particle \(P\) of weight 40 N lies at rest in equilibrium on a fixed rough horizontal surface. A force of magnitude 20 N is applied to \(P\). The force acts at angle \(\theta\) to the horizontal, as shown in Figure 2. The coefficient of friction between \(P\) and the surface is \(\mu\). Given that the particle remains at rest, show that $$\mu \geqslant \frac { \cos \theta } { 2 + \sin \theta }$$ \includegraphics[max width=\textwidth, alt={}, center]{04b73f81-3316-4f26-ad98-a7be3a4b738f-07_119_167_2615_1777}
Edexcel M1 2018 January Q3
7 marks Standard +0.3
3. Two particles \(A\) and \(B\) have mass \(2 m\) and \(k m\) respectively. The particles are moving in opposite directions along the same straight smooth horizontal line so that the particles collide directly. Immediately before the collision \(A\) has speed \(2 u\) and \(B\) has speed \(u\). The direction of motion of each particle is reversed by the collision. Immediately after the collision the speed of \(A\) is \(\frac { u } { 2 }\).
  1. Find, in terms of \(m\) and \(u\), the magnitude of the impulse exerted by \(B\) on \(A\) in the collision.
  2. Show that \(k < 5\)
Edexcel M1 2018 January Q4
8 marks Moderate -0.3
  1. A package of mass 6 kg is held at rest at a fixed point \(A\) on a rough plane. The plane is inclined at \(30 ^ { \circ }\) to the horizontal. The package is released from rest and slides down a line of greatest slope of the plane. The coefficient of friction between the package and the plane is \(\frac { 1 } { 4 }\). The package is modelled as a particle.
    1. Find the magnitude of the acceleration of the package.
    As it slides down the slope the package passes through the point \(B\), where \(A B = 10 \mathrm {~m}\).
  2. Find the speed of the package as it passes through \(B\).
Edexcel M1 2018 January Q5
12 marks Standard +0.3
5. A cyclist is travelling along a straight horizontal road. The cyclist starts from rest at point \(A\) on the road and accelerates uniformly at \(0.6 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) for 20 seconds. He then moves at constant speed for \(4 T\) seconds, where \(T < 20\). He then decelerates uniformly at \(0.3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) and after \(T\) seconds passes through point \(B\) on the road. The distance from \(A\) to \(B\) is 705 m .
  1. Sketch a speed-time graph for the motion of the cyclist between points \(A\) and \(B\).
  2. Find the value of \(T\). The cyclist continues his journey, still decelerating uniformly at \(0.3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\), until he comes to rest at point \(C\) on the road.
  3. Find the total time taken by the cyclist to travel from \(A\) to \(C\).
Edexcel M1 2018 January Q6
9 marks Moderate -0.3
  1. \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular horizontal unit vectors.]
A particle \(P\) of mass 2 kg moves under the action of two forces, \(( 2 \mathbf { i } + 3 \mathbf { j } ) \mathrm { N }\) and \(( 4 \mathbf { i } - 5 \mathbf { j } ) \mathrm { N }\).
  1. Find the magnitude of the acceleration of \(P\). At time \(t = 0 , P\) has velocity ( \(- u \mathbf { i } + u \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\), where \(u\) is a positive constant. At time \(t = T\) seconds, \(P\) has velocity \(( 10 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
  2. Find
    1. the value of \(T\),
    2. the value of \(u\).
Edexcel M1 2018 January Q7
12 marks Standard +0.3
7. A non-uniform rod \(A B\) has length 6 m and mass 8 kg . The rod rests in equilibrium, in a horizontal position, on two smooth supports at \(C\) and at \(D\), where \(A C = 1 \mathrm {~m}\) and \(D B = 1 \mathrm {~m}\), as shown in Figure 3. The magnitude of the reaction between the rod and the support at \(D\) is twice the magnitude of the reaction between the rod and the support at \(C\). The centre of mass of the rod is at \(G\), where \(A G = x \mathrm {~m}\).
  1. Show that \(x = \frac { 11 } { 3 }\). The support at \(C\) is moved to the point \(F\) on the rod, where \(A F = 2 \mathrm {~m}\). A particle of mass 3 kg is placed on the rod at \(A\). The rod remains horizontal and in equilibrium. The magnitude of the reaction between the rod and the support at \(D\) is \(k\) times the magnitude of the reaction between the rod and the support at \(F\).
  2. Find the value of \(k\).
    7. \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Figure 3} \includegraphics[alt={},max width=\textwidth]{04b73f81-3316-4f26-ad98-a7be3a4b738f-20_223_1262_127_338}
    \end{figure}
Edexcel M1 2018 January Q8
14 marks Standard +0.3
8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{04b73f81-3316-4f26-ad98-a7be3a4b738f-24_496_1143_121_404} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} One end of a light inextensible string is attached to a block \(A\) of mass 3 kg . Block \(A\) is held at rest on a smooth fixed plane. The plane is inclined at \(40 ^ { \circ }\) to the horizontal ground. The string lies along a line of greatest slope of the plane and passes over a small smooth pulley which is fixed at the top of the plane. The other end of the string is attached to a block \(B\) of mass 5 kg . Block \(B\) hangs freely at rest below the pulley, as shown in Figure 4. The system is released from rest with the string taut. By modelling the two blocks as particles,
  1. find the tension in the string as \(B\) descends. After falling for 1.5 s , block \(B\) hits the ground and is immediately brought to rest. In its subsequent motion, \(A\) does not reach the pulley.
  2. Find the speed of \(B\) at the instant it hits the ground.
  3. Find the total distance moved up the plane by \(A\) before it comes to instantaneous rest. \includegraphics[max width=\textwidth, alt={}, center]{04b73f81-3316-4f26-ad98-a7be3a4b738f-28_97_141_2519_1804}
    \includegraphics[max width=\textwidth, alt={}, center]{04b73f81-3316-4f26-ad98-a7be3a4b738f-28_125_161_2624_1779}