Questions — Edexcel M1 (599 questions)

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Edexcel M1 2020 June Q5
5. A particle \(P\) is moving in a plane with constant acceleration. The velocity, \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\), of \(P\) at time \(t\) seconds is given by $$\mathbf { v } = ( 7 - 5 t ) \mathbf { i } + ( 12 t - 20 ) \mathbf { j }$$
  1. Find the speed of \(P\) when \(t = 2\)
  2. Find, to the nearest degree, the size of the angle between the direction of motion of \(P\) and the vector \(\mathbf { j }\), when \(t = 2\) The constant acceleration of \(P\) is a m s-2
  3. Find \(\mathbf { a }\) in terms of \(\mathbf { i }\) and \(\mathbf { j }\)
  4. Find the value of \(t\) when \(P\) is moving in the direction of the vector \(( - 5 \mathbf { i } + 8 \mathbf { j } )\)
Edexcel M1 2020 June Q6
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{05cf68a3-1ba4-487f-9edd-48a246f4194f-20_328_1082_127_438} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A railway engine of mass 1500 kg is attached to a railway truck of mass 500 kg by a straight rigid coupling. The engine pushes the truck up a straight track, which is inclined to the horizontal at an angle \(\alpha\), where \(\sin \alpha = \frac { 7 } { 25 }\). The coupling is parallel to the track and parallel to the direction of motion, as shown in Figure 3. The engine produces a constant driving force of magnitude \(D\) newtons. The engine and the truck experience constant resistances to motion, from non-gravitational forces, of magnitude 1200 N and 500 N respectively. The thrust in the coupling is 2000 N . The coupling is modelled as a light rod.
  1. Find the acceleration of the engine and the truck.
  2. Find the value of \(D\).
Edexcel M1 2020 June Q7
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{05cf68a3-1ba4-487f-9edd-48a246f4194f-24_534_426_127_760} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} One end of a light inextensible string is attached to a particle \(A\) of mass \(5 m\). The other end of the string is attached to a particle \(B\) of mass \(3 m\). The string passes over a small, smooth, light fixed pulley. Particle \(A\) is held at rest with the string taut and the hanging parts of the string vertical, as shown in Figure 4. Particle A is released.
  1. Find, in terms of \(m\) and \(g\), the magnitude of the force exerted on the pulley by the string while \(A\) is falling and before \(B\) hits the pulley.
  2. State how, in your solution to part (a), you have used the fact that the pulley is smooth.
Edexcel M1 2020 June Q8
8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{05cf68a3-1ba4-487f-9edd-48a246f4194f-28_766_1587_278_182} \captionsetup{labelformat=empty} \caption{Figure 5}
\end{figure} The acceleration-time graph shown in Figure 5 represents part of a journey made by a car along a straight horizontal road. The car accelerated from rest at time \(t = 0\)
  1. Find the distance travelled by the car during the first 4 s of its journey.
  2. Find the total distance travelled by the car during the first 26s of its journey.
    VIXV SIHIANI III IM IONOOVIAV SIHI NI JYHAM ION OOVI4V SIHI NI JLIYM ION OO
    END
Edexcel M1 2021 June Q1
  1. A particle \(P\) has mass \(3 m\) and a particle \(Q\) has mass \(5 m\). The particles are moving towards each other in opposite directions along the same straight line on a smooth horizontal surface. The particles collide directly.
Immediately before the collision the speed of \(P\) is \(k u\), where \(k\) is a constant, and the speed of \(Q\) is \(2 u\). Immediately after the collision the speed of \(P\) is \(u\) and the speed of \(Q\) is \(3 u\).
The direction of motion of \(Q\) is reversed by the collision.
  1. Find, in terms of \(m\) and \(u\), the magnitude of the impulse exerted on \(Q\) by \(P\) in the collision.
  2. Find the two possible values of \(k\).
    \includegraphics[max width=\textwidth, alt={}, center]{5a2cf693-d966-4787-8778-ecc8a79a6265-03_2647_1837_118_114}
Edexcel M1 2021 June Q2
2. A car moves along a straight horizontal road with constant acceleration \(a \mathrm {~ms} ^ { - 2 }\)
where \(a > 0\) The car is modelled as a particle. At time \(t = 0\), the car passes point \(A\) and is moving with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) In the first three seconds after passing \(A\) the car travels 20 m . In the fourth second after passing \(A\) the car travels 10 m . The speed of the car as it passes point \(B\) is \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) Find the time taken for the car to travel from \(A\) to \(B\).
(8)
Edexcel M1 2021 June Q3
3. [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular horizontal unit vectors.] Three forces, \(\mathbf { F } _ { 1 } , \mathbf { F } _ { 2 }\) and \(\mathbf { F } _ { 3 }\), are given by $$\mathbf { F } _ { 1 } = ( 5 \mathbf { i } + 2 \mathbf { j } ) \mathrm { N } \quad \mathbf { F } _ { 2 } = ( - 3 \mathbf { i } + \mathbf { j } ) \mathrm { N } \quad \mathbf { F } _ { 3 } = ( a \mathbf { i } + b \mathbf { j } ) \mathrm { N }$$ where \(a\) and \(b\) are constants.
The forces \(\mathbf { F } _ { 1 } , \mathbf { F } _ { 2 }\) and \(\mathbf { F } _ { 3 }\) act on a particle \(P\) of mass 4 kg .
Given that \(P\) rests in equilibrium on a smooth horizontal surface under the action of these three forces,
  1. find the size of the angle between the direction of \(\mathbf { F } _ { 3 }\) and the direction of \(- \mathbf { j }\). The force \(\mathbf { F } _ { 3 }\) is now removed and replaced by the force \(\mathbf { F } _ { 4 }\) given by \(\mathbf { F } _ { 4 } = \lambda ( \mathbf { i } + 3 \mathbf { j } )\) N, where \(\lambda\) is a positive constant. When the three forces \(\mathbf { F } _ { 1 } , \mathbf { F } _ { 2 }\) and \(\mathbf { F } _ { 4 }\) act on \(P\), the acceleration of \(P\) has magnitude \(3.25 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)
  2. Find the value of \(\lambda\).
Edexcel M1 2021 June Q4
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5a2cf693-d966-4787-8778-ecc8a79a6265-12_647_396_251_776} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a large bucket used by a crane on a building site to move materials between the ground and the top of the building. The mass of the bucket is 15 kg . The bucket is attached to a vertical cable with the bottom of the bucket horizontal. The cable is modelled as light and inextensible. When the bucket is on the ground, a bag of cement of mass 25 kg is placed in the bucket. The bucket with the bag of cement moves vertically upwards with constant acceleration \(0.2 \mathrm {~ms} ^ { - 2 }\). Air resistance is modelled as being negligible.
  1. Find the tension in the cable. At the top of the building, the bag of cement is removed. A box of tools of mass 12 kg is now placed in the bucket. Later on the bucket with the box of tools is moving vertically downwards with constant deceleration \(0.1 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). Air resistance is again modelled as being negligible.
  2. Find the magnitude of the normal reaction between the bucket and the box of tools.
Edexcel M1 2021 June Q5
  1. \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular horizontal unit vectors.]
A particle \(P\) is moving with constant acceleration. At 2 pm , the velocity of \(P\) is \(( 3 \mathbf { i } + 5 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\) and at 2.30 pm the velocity of \(P\) is \(( \mathbf { i } + 7 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\) At time \(T\) hours after \(2 \mathrm { pm } , P\) is moving in the direction of the vector \(( - \mathbf { i } + 2 \mathbf { j } )\)
  1. Find the value of \(T\). Another particle, \(Q\), has velocity \(\mathbf { v } _ { Q } \mathrm {~km} \mathrm {~h} ^ { - 1 }\) at time \(t\) hours after 2 pm , where $$\mathbf { v } _ { Q } = ( - 4 - 2 t ) \mathbf { i } + ( \mu + 3 t ) \mathbf { j }$$ and \(\mu\) is a constant. Given that there is an instant when the velocity of \(P\) is equal to the velocity of \(Q\),
  2. find the value of \(\mu\).
Edexcel M1 2021 June Q6
  1. A fixed rough plane is inclined at an angle \(\theta\) to the horizontal, where \(\tan \theta = \frac { 5 } { 12 }\)
A particle of mass 6 kg is projected with speed \(5 \mathrm {~ms} ^ { - 1 }\) from a point \(A\) on the plane, up a line of greatest slope of the plane. The coefficient of friction between the particle and the plane is \(\frac { 1 } { 4 }\)
  1. Find the magnitude of the frictional force acting on the particle as it moves up the plane. The particle comes to instantaneous rest at the point \(B\).
  2. Find the distance \(A B\). The particle now slides down the plane from \(B\). At the instant when the particle passes through the point \(C\) on the plane, the speed of the particle is again \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
  3. Find the distance \(B C\). \includegraphics[max width=\textwidth, alt={}, center]{5a2cf693-d966-4787-8778-ecc8a79a6265-23_2647_1835_118_116}
Edexcel M1 2021 June Q7
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5a2cf693-d966-4787-8778-ecc8a79a6265-24_191_1136_255_406} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A non-uniform beam \(A B\), of mass 60 kg and length \(8 a\) metres, rests in equilibrium in a horizontal position on two vertical supports. One support is at \(C\), where \(A C = a\) metres and the other support is at \(D\), where \(D B = 2 a\) metres, as shown in Figure 2. The magnitude of the normal reaction between the beam and the support at \(D\) is three times the magnitude of the normal reaction between the beam and the support at \(C\). By modelling the beam as a non-uniform rod whose centre of mass is at a distance \(x\) metres from \(A\),
  1. find an expression for \(x\) in terms of \(a\). A box of mass \(M \mathrm {~kg}\) is placed on the beam at \(E\), where \(A E = 2 a\) metres.
    The beam remains in equilibrium in a horizontal position.
    The magnitude of the normal reaction between the beam and the support at \(C\) is now equal to the magnitude of the normal reaction between the beam and the support at \(D\). By modelling the box as a particle,
  2. find the value of \(M\).
Edexcel M1 2021 June Q8
8. Two trams, tram \(A\) and tram \(B\), run on parallel straight horizontal tracks. Initially the two trams are at rest in the depot and level with each other. At time \(t = 0 , \operatorname { tram } A\) starts to move. Tram \(A\) moves with constant acceleration \(2 \mathrm {~ms} ^ { - 2 }\) for 5 seconds and then continues to move along the track at constant speed. At time \(t = 20\) seconds, tram \(B\) starts from rest and moves in the same direction as tram \(A\). Tram \(B\) moves with constant acceleration \(3 \mathrm {~ms} ^ { - 2 }\) for 4 seconds and then continues to move along the track at constant speed. The trams are modelled as particles.
  1. Sketch, on the same axes, a speed-time graph for the motion of tram \(A\) and a speed-time graph for the motion of tram \(B\), from \(t = 0\) to the instant when tram \(B\) overtakes \(\operatorname { tram } A\). At the instant when the two trams are moving with the same speed, \(\operatorname { tram } A\) is \(d\) metres in front of tram \(B\).
  2. Find the value of \(d\).
  3. Find the distance of the trams from the depot at the instant when tram \(B\) overtakes \(\operatorname { tram } A\).
    \includegraphics[max width=\textwidth, alt={}, center]{5a2cf693-d966-4787-8778-ecc8a79a6265-32_2647_1835_118_116}
    VALV SIHI NI IIIIIM ION OC
    VALV SIHI NI IMIMM ION OO
    VIUV SIHI NI JIIXM ION OC
Edexcel M1 2022 June Q1
  1. Two particles, \(P\) and \(Q\), are moving towards each other in opposite directions along the same straight line when they collide directly. Immediately before the collision the speed of \(Q\) is \(2 u\). The mass of \(Q\) is \(3 m\) and the magnitude of the impulse exerted by \(P\) on \(Q\) in the collision is \(4 m u\).
Find
  1. the speed of \(Q\) immediately after the collision,
  2. the direction of motion of \(Q\) immediately after the collision.
Edexcel M1 2022 June Q2
2. A motorbike is moving with constant acceleration along a straight horizontal road. The motorbike passes a point \(P\) and 10 seconds later passes a point \(Q\). The speed of the motorbike as it passes \(Q\) is \(28 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
Given that \(P Q = 220 \mathrm {~m}\),
  1. find the acceleration of the motorbike,
  2. find the distance travelled by the motorbike during the fifth second after passing \(P\) VILV SIHI NI IIII M I ON OC
    VARV SIHI NI JLIUMI ON OC
    VIIV SIHIL NI IMINM ION OC
Edexcel M1 2022 June Q3
3. A tractor of mass 6 tonnes is dragging a large block of mass 2 tonnes along rough horizontal ground. The cable connecting the tractor to the block is horizontal and parallel to the direction of motion. The cable is modelled as being light and inextensible.
The driving force of the tractor is 7400 N and the resistance to the motion of the tractor is 200 N . The resistance to the motion of the block is \(R\) newtons, where \(R\) is a constant. Given that the tension in the cable is 6000 N and the tractor is accelerating,
  1. find the value of \(R\).
  2. State how you have used the fact that the cable is modelled as being inextensible.
    VIIHV SIHI NI IIIHM IONOOCVIAV SIMI NI III IM I O N OAVI4V SIHI NI JIIIM ION OC
    Q
Edexcel M1 2022 June Q4
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{61cb5bce-2fad-48f0-b6a4-e9899aa0acec-10_209_1017_255_466} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A small block of mass 5 kg lies at rest on a rough horizontal plane.
The coefficient of friction between the block and the plane is \(\frac { 3 } { 7 }\)
A force of magnitude \(P\) newtons is applied to the block in a direction which makes an angle of \(30 ^ { \circ }\) with the plane, as shown in Figure 1. The block is modelled as a particle.
Given that \(P = 14\)
  1. find the magnitude of the frictional force exerted on the block by the plane and describe what happens to the block, justifying your answer.
    (6) The value of \(P\) is now changed so that the block is on the point of slipping along the plane.
  2. Find the value of \(P\)
Edexcel M1 2022 June Q5
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{61cb5bce-2fad-48f0-b6a4-e9899aa0acec-14_296_1283_255_333} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A uniform rod \(A B\) has length 5 m and mass 5 kg . The rod rests in equilibrium in a horizontal position on two supports \(C\) and \(D\), where \(A C = 1 \mathrm {~m}\) and \(D B = 2 \mathrm {~m}\), as shown in Figure 2 . A particle of mass 10 kg is placed on the rod at \(A\) and a particle of mass \(M \mathrm {~kg}\) is placed on the rod at \(B\). The rod remains horizontal and in equilibrium.
  1. Find, in terms of \(M\), the magnitude of the reaction on the rod at \(C\).
  2. Find, in terms of \(M\), the magnitude of the reaction on the rod at \(D\).
  3. Hence, or otherwise, find the range of possible values of \(M\).
    \includegraphics[max width=\textwidth, alt={}, center]{61cb5bce-2fad-48f0-b6a4-e9899aa0acec-14_2256_51_310_1983}
Edexcel M1 2022 June Q6
6. A particle \(P\) is moving with constant acceleration. At time \(t = 1\) second, \(P\) has velocity \(( - \mathbf { i } + 4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\)
At time \(t = 4\) seconds, \(P\) has velocity \(( 5 \mathbf { i } - 8 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\)
Find the speed of \(P\) at time \(t = 3.5\) seconds.
Edexcel M1 2022 June Q7
7. Two small children, Ajaz and Beth, are running a 100 m race along a straight horizontal track. They both start from rest, leaving the start line at the same time. Ajaz accelerates at \(0.8 \mathrm {~ms} ^ { - 2 }\) up to a speed of \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and then maintains this speed until he crosses the finish line. Beth accelerates at \(1 \mathrm {~ms} ^ { - 2 }\) for \(T\) seconds and then maintains a constant speed until she crosses the finish line. Ajaz and Beth cross the finish line at the same time.
  1. Sketch, on the same axes, a speed-time graph for each child, from the instant when they leave the start line to the instant when they cross the finish line.
  2. Find the time taken by Ajaz to complete the race.
  3. Find the value of \(T\)
  4. Find the difference in the speeds of the two children as they cross the finish line.
Edexcel M1 2022 June Q8
8. [In this question, \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors directed due east and due north respectively and position vectors are given relative to a fixed origin \(O\).] Two boats, \(P\) and \(Q\), are moving with constant velocities.
The velocity of \(P\) is \(15 \mathbf { i } \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the velocity of \(Q\) is \(( 20 \mathbf { i } - 20 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\)
  1. Find the direction in which \(Q\) is travelling, giving your answer as a bearing. The boats are modelled as particles.
    At time \(t = 0 , P\) is at the origin \(O\) and \(Q\) is at the point with position vector \(200 \mathbf { j } \mathrm {~m}\). At time \(t\) seconds, the position vector of \(P\) is \(\mathbf { p m }\) and the position vector of \(Q\) is \(\mathbf { q m }\).
  2. Show that $$\overrightarrow { P Q } = [ 5 t \mathbf { i } + ( 200 - 20 t ) \mathbf { j } ] \mathrm { m }$$
  3. Find the bearing of \(P\) from \(Q\) when \(t = 10\)
  4. Find the distance between \(P\) and \(Q\) when \(Q\) is north east of \(P\)
  5. Find the times when \(P\) and \(Q\) are 200 m apart.
Edexcel M1 2023 June Q1
  1. A particle \(A\) has mass 4 kg and a particle \(B\) has mass 2 kg .
The particles move towards each other in opposite directions along the same straight line on a smooth horizontal table and collide directly. Immediately before the collision, the speed of \(A\) is \(2 u \mathrm {~ms} ^ { - 1 }\) and the speed of \(B\) is \(3 u \mathrm {~ms} ^ { - 1 }\)
Immediately after the collision, the speed of \(B\) is \(2 u \mathrm {~ms} ^ { - 1 }\)
The direction of motion of \(B\) is reversed by the collision.
  1. Find, in terms of \(u\), the speed of \(A\) immediately after the collision.
  2. State the direction of motion of \(A\) immediately after the collision.
  3. Find, in terms of \(u\), the magnitude of the impulse received by \(B\) in the collision. State the units of your answer. \section*{[In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal perpendicular unit vectors.]}
Edexcel M1 2023 June Q2
  1. A particle \(P\) rests in equilibrium on a smooth horizontal plane.
A system of three forces, \(\mathbf { F } _ { 1 } \mathrm {~N} , \mathbf { F } _ { 2 } \mathrm {~N}\) and \(\mathbf { F } _ { 3 } \mathrm {~N}\) where $$\begin{aligned} & \mathbf { F } _ { 1 } = ( 3 c \mathbf { i } + 4 c \mathbf { j } )
& \mathbf { F } _ { 2 } = ( - 14 \mathbf { i } + 7 \mathbf { j } ) \end{aligned}$$ is applied to \(P\).
Given that \(P\) remains in equilibrium,
  1. find \(\mathbf { F } _ { 3 }\) in terms of \(c\), \(\mathbf { i }\) and \(\mathbf { j }\). The force \(\mathbf { F } _ { 3 }\) is removed from the system.
    Given that \(c = 2\)
  2. find the size of the angle between the direction of \(\mathbf { i }\) and the direction of the resultant force acting on \(P\). The mass of \(P\) is \(m \mathrm {~kg}\).
    Given that the magnitude of the acceleration of \(P\) is \(8.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)
  3. find the value of \(m\).
Edexcel M1 2023 June Q3
  1. Two students observe a book of mass 0.2 kg fall vertically from rest from a shelf that is 1.5 m above the floor.
Student \(A\) suggests that the book is modelled as a particle falling freely under gravity.
  1. Use student \(A\) 's model to find the time taken for the book to reach the floor. Student \(B\) suggests an improved model where the book is modelled as a particle experiencing a constant resistance to motion of magnitude \(R\) newtons. Given that the time taken for the book to reach the floor is 0.6 seconds,
  2. use student \(B\) 's model to find the value of \(R\)
Edexcel M1 2023 June Q4
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f2737a11-4a15-41e9-9f87-31a705a8948b-08_625_1488_246_287} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a beam \(A B\), of mass \(m \mathrm {~kg}\) and length 2 m , suspended by two light vertical ropes.
The ropes are attached to the points \(C\) and \(D\) on the beam, where \(A C = 0.6 \mathrm {~m}\) and \(D B = 0.2 \mathrm {~m}\)
The beam is in equilibrium in a horizontal position.
A particle of mass pmkg is attached to the beam at \(A\) and the beam remains in equilibrium in a horizontal position. The beam is modelled as a uniform rod.
  1. Given that the tension in the rope attached at \(C\) is four times the tension in the rope attached at \(D\), use the model to find the exact value of \(p\). The particle of mass \(p m \mathrm {~kg}\) at \(A\) is removed and replaced by a particle of mass \(q m \mathrm {~kg}\) at \(A\).
    The beam remains in equilibrium in a horizontal position but is now on the point of tilting.
  2. Using the model, find the exact value of \(q\)
  3. State how you have used the modelling assumption that the beam is uniform.
Edexcel M1 2023 June Q5
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f2737a11-4a15-41e9-9f87-31a705a8948b-12_629_1251_244_406} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} The speed-time graph in Figure 2 illustrates the motion of a car travelling along a straight horizontal road.
At time \(t = 0\), the car starts from rest and accelerates uniformly for 30 s until it reaches a speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
The car then travels at a constant speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) until time \(t = T\) seconds.
  1. Show that the distance travelled by the car between \(t = 0\) and \(t = T\) seconds is \(V ( T - 15 )\) metres. A motorbike also travels along the same road.
    • The motorbike starts from rest at time \(\boldsymbol { t } = \mathbf { 1 0 } \mathbf { s }\) and accelerates uniformly for 40 s
    • The acceleration of the motorbike is the same as the acceleration of the car
    • The motorbike then travels at a constant speed for a further 10 s before decelerating uniformly until it reaches a speed of \(V \mathrm {~ms} ^ { - 1 }\) at time \(T\) seconds
    • On Figure 2, sketch a speed-time graph for the motion of the motorbike.
      [0pt] [If you need to redraw your sketch, there is a copy of Figure 2 on page 15.]
    • Show that the constant speed of the motorbike is \(\frac { 4 V } { 3 } \mathrm {~ms} ^ { - 1 }\)
    At time \(t = T\) seconds, the distance travelled by each vehicle is the same.
  2. Find the value of \(T\) \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{f2737a11-4a15-41e9-9f87-31a705a8948b-15_643_1266_1882_402} \captionsetup{labelformat=empty} \caption{Figure 2}
    \end{figure}