Questions — Edexcel M1 (599 questions)

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Edexcel M1 2018 October Q1
  1. A particle \(P\) of mass 0.8 kg is moving along a straight horizontal line on a smooth hoizontal surface with speed \(4 \mathrm {~ms} ^ { - 1 }\). A second particle \(Q\) of mass 2 kg is moving, in the opposite direction to \(P\), along the same straight line with speed \(2 \mathrm {~ms} ^ { - 1 }\). The particles collide directly. Immediately after the collision the direction of motion of each particle is reversed and the speed of \(P\) is \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
    1. Find the speed of \(Q\) immediately after the collision.
    2. Find the magnitude of the impulse exerted by \(Q\) on \(P\) in the collision, stating the units of your answer.
    VILU SIHI NI III M I ION OCVIIV 5141 NI 311814 ION OCVI4V SIHI NI JIIYM ION OC
    Figure 1 A non-uniform plank \(A B\) has weight 60 N and length 5 m . The plank rests horizontally in equilibrium on two smooth supports at \(A\) and \(C\), where \(A C = 3 \mathrm {~m}\), as shown in Figure 1. A parcel of weight 12 N is placed on the plank at \(B\) and the plank remains horizontal and in equilibrium. The magnitude of the reaction of the support at \(A\) on the plank is half the magnitude of the reaction of the support at \(C\) on the plank. By modelling the plank as a non-uniform rod and the parcel as a particle,
  2. find the distance of the centre of mass of the plank from \(A\).
  3. State briefly how you have used the modelling assumption
    1. that the parcel is a particle,
    2. that the plank is a rod.
Edexcel M1 2018 October Q2
2.
\includegraphics[max width=\textwidth, alt={}, center]{5f2d38d9-b719-4205-8cb0-caa959afc46f-04_269_1175_296_375}
Edexcel M1 2018 October Q3
  1. At time \(t = 0\), a stone is thrown vertically upwards with speed \(19.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point \(A\) which is \(h\) metres above horizontal ground. At time \(t = 3 \mathrm {~s}\), another stone is released from rest from a point \(B\) which is also \(h\) metres above the same horizontal ground. Both stones hit the ground at time \(t = T\) seconds. The motion of each stone is modelled as that of a particle moving freely under gravity.
Find
  1. the value of \(T\),
  2. the value of \(h\).
    VILU SIHI NI III M I ION OCVIIV 5141 NI JINAM ION OCVI4V SIHI NI JIIYM ION OO
Edexcel M1 2018 October Q4
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5f2d38d9-b719-4205-8cb0-caa959afc46f-12_540_584_294_680} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A particle \(P\) of mass \(m \mathrm {~kg}\) is attached to one end of a light inextensible string of length 2.5 m . The other end of the string is attached to a fixed point \(A\) on a vertical wall. The tension in the string is 16 N . The particle is held in equilibrium by a force of magnitude \(F\) newtons, acting in the vertical plane which is perpendicular to the wall and contains the string. This force acts in a direction perpendicular to the string, as shown in Figure 2. Given that the horizontal distance of \(P\) from the wall is 1.5 m , find
  1. the value of \(F\),
  2. the value of \(m\).
    \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{5f2d38d9-b719-4205-8cb0-caa959afc46f-16_186_830_292_557} \captionsetup{labelformat=empty} \caption{Figure 3}
    \end{figure} Two posts, \(A\) and \(B\), are fixed at the side of a straight horizontal road and are 816 m apart, as shown in Figure 3. A car and a van are at rest side by side on the road and level with \(A\). The car and the van start to move at the same time in the direction \(A B\). The car accelerates from rest with constant acceleration until it reaches a speed of \(24 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The car then moves at a constant speed of \(24 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The van accelerates from rest with constant acceleration for 12 s until it reaches a speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The van then moves at a constant speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). When the car has been moving at \(24 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for 30 s , the van draws level with the car at \(B\), and each vehicle has then travelled a distance of 816 m .
    (a) Sketch, on the same diagram, a speed-time graph for the motion of each vehicle from \(A\) to \(B\).
    (b) Find the time for which the car is accelerating.
    (c) Find the value of \(V\).
Edexcel M1 2018 October Q5
5.
[In this question the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal vectors due east and due north respectively and position vectors are given relative to a fixed origin.]
Edexcel M1 2018 October Q6
6. The point \(A\) on a horizontal playground has position vector \(( 3 \mathbf { i } - 2 \mathbf { j } ) \mathrm { m }\). At time \(t = 0\), a girl kicks a ball from \(A\). The ball moves horizontally along the playground with constant velocity \(( 4 \mathbf { i } + 5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). Modelling the ball as a particle, find
  1. the speed of the ball,
  2. the position vector of the ball at time \(t\) seconds. The point \(B\) on the playground has position vector \(( \mathbf { i } + 6 \mathbf { j } ) \mathrm { m }\). At time \(t = T\) seconds, the ball is due east of \(B\).
  3. Find the value of \(T\). A boy is running due east with constant speed \(\nu \mathrm { ms } ^ { - 1 }\). At the instant when the girl kicks the ball from \(A\), the boy is at \(B\). Given that the boy intercepts the ball,
  4. find the value of \(v\). \includegraphics[max width=\textwidth, alt={}, center]{5f2d38d9-b719-4205-8cb0-caa959afc46f-23_68_47_2617_1886}
Edexcel M1 2018 October Q7
7. A truck of mass 1600 kg is towing a car of mass 960 kg along a straight horizontal road. The truck and the car are joined by a light rigid tow bar. The tow bar is horizontal and is parallel to the direction of motion. The truck and the car experience constant resistances to motion of magnitude 640 N and \(R\) newtons respectively. The truck's engine produces a constant driving force of magnitude 2100 N . The magnitude of the acceleration of the truck and the car is \(0.4 \mathrm {~ms} ^ { - 2 }\).
  1. Show that \(R = 436\)
  2. Find the tension in the tow bar. The two vehicles come to a hill inclined at an angle \(\alpha\) to the horizontal where \(\sin \alpha = \frac { 1 } { 15 }\). The truck and the car move down a line of greatest slope of the hill with the tow bar parallel to the direction of motion. The truck's engine produces a constant driving force of magnitude 2100 N . The magnitudes of the resistances to motion on the truck and the car are 640 N and 436 N respectively.
  3. Find the magnitude of the acceleration of the truck and the car as they move down the hill.
    \includegraphics[max width=\textwidth, alt={}, center]{5f2d38d9-b719-4205-8cb0-caa959afc46f-27_67_59_2654_1886}
Edexcel M1 2018 October Q8
8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5f2d38d9-b719-4205-8cb0-caa959afc46f-28_268_634_292_657} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} A rough plane is inclined at \(30 ^ { \circ }\) to the horizontal. A particle \(P\) of mass 0.5 kg is held at rest on the plane by a horizontal force of magnitude 5 N , as shown in Figure 4. The force acts in a vertical plane containing a line of greatest slope of the inclined plane. The particle is on the point of moving up the plane.
  1. Find the magnitude of the normal reaction of the plane on \(P\).
  2. Find the coefficient of friction between \(P\) and the plane. The force of magnitude 5 N is now removed and \(P\) accelerates from rest down the plane.
  3. Find the speed of \(P\) after it has travelled 3 m down the plane.
Edexcel M1 2021 October Q1
1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{151d9232-5a78-4bc1-a57e-6c9cae80e473-02_298_1288_264_328} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A non-uniform rod \(A B\) has length 9 m and mass \(M \mathrm {~kg}\).
The rod rests in equilibrium in a horizontal position on two supports, one at \(C\) where \(A C = 2.5 \mathrm {~m}\) and the other at \(D\) where \(D B = 2 \mathrm {~m}\), as shown in Figure 1 . The magnitude of the force acting on the rod at \(D\) is twice the magnitude of the force acting on the \(\operatorname { rod }\) at \(C\). The centre of mass of the rod is \(d\) metres from \(A\).
Find the value of \(d\).
VIAV SIHI NI III IM IONOOVIAV SIHI NI III IM I ON OOVIAV SIHI NI III HM ION OC
Edexcel M1 2021 October Q2
2. A particle \(P\) of mass \(2 m\) is moving on a rough horizontal plane when it collides directly with a particle \(Q\) of mass \(4 m\) which is at rest on the plane. The speed of \(P\) immediately before the collision is \(3 u\). The speed of \(Q\) immediately after the collision is \(2 u\).
  1. Find, in terms of \(u\), the speed of \(P\) immediately after the collision.
  2. State clearly the direction of motion of \(P\) immediately after the collision. Following the collision, \(Q\) comes to rest after travelling a distance \(\frac { 6 u ^ { 2 } } { g }\) along the plane. The coefficient of friction between \(Q\) and the plane is \(\mu\).
  3. Find the value of \(\mu\).
Edexcel M1 2021 October Q3
3. A car is moving at a constant speed of \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) along a straight horizontal road. The car is modelled as a particle.
At time \(t = 0\), the car is at the point \(A\) and the driver sees a road sign 48 m ahead.
Let \(t\) seconds be the time that elapses after the car passes \(A\).
In a first model, the car is assumed to decelerate uniformly at \(6 \mathrm {~ms} ^ { - 2 }\) from \(A\) until the car reaches the road sign.
  1. Use this first model to find the speed of the car as it reaches the sign. The road sign indicates that the speed limit immediately after the sign is \(13 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
    In a second model, the car is assumed to decelerate uniformly at \(6 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) from \(A\) until it reaches a speed of \(13 \mathrm {~ms} ^ { - 1 }\). The car then maintains this speed until it reaches the road sign.
  2. Use this second model to find the value of \(t\) at which the car reaches the sign. In a third model, the car is assumed to move with constant speed \(25 \mathrm {~ms} ^ { - 1 }\) from \(A\) until time \(t = 0.2\), the car then decelerates uniformly at \(6 \mathrm {~ms} ^ { - 2 }\) until it reaches a speed of \(13 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The car then maintains this speed until it reaches the road sign.
  3. Use this third model to find the value of \(t\) at which the car reaches the sign.
Edexcel M1 2021 October Q4
  1. The position vector, \(\mathbf { r }\) metres, of a particle \(P\) at time \(t\) seconds, relative to a fixed origin \(O\), is given by
$$\mathbf { r } = ( t - 3 ) \mathbf { i } + ( 1 - 2 t ) \mathbf { j }$$
  1. Find, to the nearest degree, the size of the angle between \(\mathbf { r }\) and the vector \(\mathbf { j }\), when \(t = 2\)
  2. Find the values of \(t\) for which the distance of \(P\) from \(O\) is 2.5 m .
Edexcel M1 2021 October Q5
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{151d9232-5a78-4bc1-a57e-6c9cae80e473-18_440_230_248_856} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A small bead of mass 0.2 kg is attached to the end \(P\) of a light rod \(P Q\). The bead is threaded onto a fixed vertical rough wire. The bead is held in equilibrium with the \(\operatorname { rod } P Q\) inclined to the wire at an angle \(\alpha\), where \(\tan \alpha = \frac { 4 } { 3 }\), as shown in Figure 2. The thrust in the rod is \(T\) newtons.
The bead is modelled as a particle.
  1. Find the magnitude and direction of the friction force acting on the bead when \(T = 2.5\) The coefficient of friction between the bead and the wire is \(\mu\).
    Given that the greatest possible value of \(T\) is 6.125
  2. find the value of \(\mu\).
Edexcel M1 2021 October Q6
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{151d9232-5a78-4bc1-a57e-6c9cae80e473-22_428_993_251_479} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A small ball is thrown vertically upwards at time \(t = 0\) from a point \(A\) which is above horizontal ground. The ball hits the ground 7 s later. The ball is modelled as a particle moving freely under gravity.
The velocity-time graph shown in Figure 3 represents the motion of the ball for \(0 \leqslant t \leqslant 7\)
  1. Find the speed with which the ball is thrown.
  2. Find the height of \(A\) above the ground.
Edexcel M1 2021 October Q7
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{151d9232-5a78-4bc1-a57e-6c9cae80e473-24_446_624_260_708} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} One end of a light inextensible string is attached to a particle \(A\) of mass \(2 m\). The other end of the string is attached to a particle \(B\) of mass \(3 m\). The string passes over a small, smooth, light pulley \(P\) which is fixed at the top of a rough inclined plane. The plane is inclined to the horizontal at an angle \(\alpha\), where \(\tan \alpha = \frac { 3 } { 4 }\) Particle \(A\) is held at rest on the plane with the string taut and \(B\) hanging freely below \(P\), as shown in Figure 4. The section of the string \(A P\) is parallel to a line of greatest slope of the plane. The coefficient of friction between \(A\) and the plane is \(\frac { 1 } { 2 }\)
Particle \(A\) is released and begins to move up the plane.
For the motion before \(A\) reaches the pulley,
    1. write down an equation of motion for \(A\),
    2. write down an equation of motion for \(B\),
  2. find, in terms of \(g\), the acceleration of \(A\),
  3. find the magnitude of the force exerted on the pulley by the string.
  4. State how you have used the information that \(P\) is a smooth pulley.
Edexcel M1 2021 October 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.] At 7 am a ship leaves a port and moves with constant velocity. The position vector of the port is \(( - 2 \mathbf { i } + 9 \mathbf { j } ) \mathrm { km }\). At 7.36 am the ship is at the point with position vector \(( 4 \mathbf { i } + 6 \mathbf { j } ) \mathrm { km }\).
  1. Show that the velocity of the ship is \(( 10 \mathbf { i } - 5 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }\)
  2. Find the position vector of the ship \(t\) hours after leaving port. At 8.48 am a passenger on the ship notices that a lighthouse is due east of the ship. At 9 am the same passenger notices that the lighthouse is now north east of the ship.
  3. Find the position vector of the lighthouse.
  4. Find the position vector of the ship when it is due south of the lighthouse.
    \includegraphics[max width=\textwidth, alt={}]{151d9232-5a78-4bc1-a57e-6c9cae80e473-32_2258_53_308_1980}
Edexcel M1 2022 October Q1
  1. A railway truck \(S\) of mass 20 tonnes is moving along a straight horizontal track when it collides with another railway truck \(T\) of mass 30 tonnes which is at rest. Immediately before the collision the speed of \(S\) is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
    As a result of the collision, the two railway trucks join together.
    Find
    1. the common speed of the railway trucks immediately after the collision,
    2. the magnitude of the impulse exerted on \(S\) in the collision, stating the units of your answer.
Edexcel M1 2022 October Q2
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2633b149-96db-4b80-96c2-e3e6bfbee174-04_515_1282_269_331} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A uniform rod \(A B\) has length \(2 a\) and mass \(M\). The rod is held in equilibrium in a horizontal position by two vertical light strings which are attached to the rod at \(C\) and \(D\), where \(A C = \frac { 2 } { 5 } a\) and \(D B = \frac { 3 } { 5 } a\), as shown in Figure 1. A particle \(P\) is placed on the rod at \(B\).
The rod remains horizontal and in equilibrium.
  1. Find, in terms of \(M\), the largest possible mass of the particle \(P\) Given that the mass of \(P\) is \(\frac { 1 } { 2 } M\)
  2. find, in terms of \(M\) and \(g\), the tension in the string that is attached to the rod at \(C\).
Edexcel M1 2022 October Q3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2633b149-96db-4b80-96c2-e3e6bfbee174-08_301_636_287_657} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A rough plane is inclined to the horizontal at an angle \(\alpha\), where \(\tan \alpha = \frac { 3 } { 4 }\)
A particle \(P\) of mass 2 kg is held in equilibrium on the plane by a horizontal force of magnitude \(X\) newtons, as shown in Figure 2. The force acts in a vertical plane which contains a line of greatest slope of the inclined plane.
  1. Show that when \(X = 14.7\) there is no frictional force acting on \(P\) The coefficient of friction between \(P\) and the plane is 0.5
  2. Find the smallest possible value of \(X\).
    VIAV SIHI NI IIIIM I I N OC
    VARY SIMI NI EIIIM I ON OC
    VILV SIMI NI III M I I N OC \includegraphics[max width=\textwidth, alt={}, center]{2633b149-96db-4b80-96c2-e3e6bfbee174-11_88_63_2631_1886}
Edexcel M1 2022 October Q4
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2633b149-96db-4b80-96c2-e3e6bfbee174-12_543_264_296_842} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Two children, Alan and Bhavana, are standing on the horizontal floor of a lift, as shown in Figure 3. The lift has mass 250 kg . The lift is raised vertically upwards with constant acceleration by a vertical cable which is attached to the top of the lift. The cable is modelled as being light and inextensible. While the lift is accelerating upwards, the tension in the cable is 3616 N . As the lift accelerates upwards, the floor of the lift exerts a force of magnitude 565 N on Alan and a force of magnitude 226 N on Bhavana. Air resistance is modelled as being negligible and Alan and Bhavana are modelled as particles.
  1. By considering the forces acting on the lift only, find the acceleration of the lift.
  2. Find the mass of Alan.
Edexcel M1 2022 October Q5
5. A small ball is projected vertically upwards with speed \(29.4 \mathrm {~ms} ^ { - 1 }\) from a point \(A\) which is 19.6 m above horizontal ground. The ball is modelled as a particle moving freely under gravity until it hits the ground. It is assumed that the ball does not rebound.
  1. Find the distance travelled by the ball while its speed is less than \(14.7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
  2. Find the time for which the ball is moving with a speed of more than \(29.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
  3. Sketch a speed-time graph for the motion of the ball from the instant when it is projected from \(A\) to the instant when it hits the ground. Show clearly where your graph meets the axes.
    Q
    7
Edexcel M1 2022 October Q7
7
6. [In this question, \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors.] A particle \(A\) of mass 0.5 kg is at rest on a smooth horizontal plane.
At time \(t = 0\), two forces, \(\mathbf { F } _ { 1 } = ( - 3 \mathbf { i } + 2 \mathbf { j } ) \mathrm { N }\) and \(\mathbf { F } _ { 2 } = ( p \mathbf { i } + q \mathbf { j } ) \mathrm { N }\), where \(p\) and \(q\) are constants, are applied to \(A\). Given that \(A\) moves in the direction of the vector \(( \mathbf { i } - 2 \mathbf { j } )\),
  1. show that \(2 p + q - 4 = 0\) Given that \(p = 5\)
  2. find the speed of \(A\) at time \(t = 4\) seconds.
    7. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{2633b149-96db-4b80-96c2-e3e6bfbee174-24_451_851_310_493} \captionsetup{labelformat=empty} \caption{Figure 4}
    \end{figure} A particle \(P\) of mass \(m\) is attached to one end of a light inextensible string. Another particle \(Q\), also of mass \(m\), is attached to the other end of the string. The string passes over a small smooth pulley which is fixed at the edge of a rough horizontal table. Particle \(Q\) is held at rest on the table and particle \(P\) hangs vertically below the pulley with the string taut, as shown in Figure 4. The pulley, \(P\) and \(Q\) all lie in the same vertical plane.
    The coefficient of friction between \(Q\) and the table is \(\mu\), where \(\mu < 1\)
    Particle \(Q\) is released from rest.
    The tension in the string before \(Q\) hits the pulley is \(k m g\), where \(k\) is a constant.
  3. Find \(k\) in terms of \(\mu\). Given that \(Q\) is initially a distance \(d\) from the pulley,
  4. find, in terms of \(d , g\) and \(\mu\), the time taken by \(Q\), after release, to reach the pulley.
  5. Describe what would happen if \(\mu \geqslant 1\), giving a reason for your answer.
Edexcel M1 2022 October 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 ships, \(A\) and \(B\), are moving with constant velocities.
The velocity of \(A\) is \(( 3 \mathbf { i } + 12 \mathbf { j } ) \mathrm { kmh } ^ { - 1 }\) and the velocity of \(B\) is \(( p \mathbf { i } + q \mathbf { j } ) \mathrm { kmh } ^ { - 1 }\)
  1. Find the speed of \(A\). The ships are modelled as particles.
    At 12 noon, \(A\) is at the point with position vector \(( - 9 \mathbf { i } + 6 \mathbf { j } ) \mathrm { km }\) and \(B\) is at the point with position vector \(( 16 \mathbf { i } + 6 \mathbf { j } ) \mathrm { km }\). At time \(t\) hours after 12 noon, $$\overrightarrow { A B } = [ ( 25 - 12 t ) \mathbf { i } - 9 t \mathbf { j } ] \mathrm { km }$$
  2. Find the value of \(p\) and the value of \(q\).
  3. Find the bearing of \(A\) from \(B\) when the ships are 15 km apart, giving your answer to the nearest degree.
    \includegraphics[max width=\textwidth, alt={}, center]{2633b149-96db-4b80-96c2-e3e6bfbee174-32_120_150_2508_1804}
    \includegraphics[max width=\textwidth, alt={}, center]{2633b149-96db-4b80-96c2-e3e6bfbee174-32_143_191_2633_1779}
Edexcel M1 2023 October Q1
1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{017cc2b0-9ec3-45ff-94c0-9d989badfd5d-02_529_1362_246_349} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a beam \(A B\) with weight 24 N and length 6 m .
The beam is suspended by two light vertical ropes. The ropes are attached to the points \(C\) and \(D\) on the beam where \(A C = x\) metres and \(C D = 2 \mathrm {~m}\). The tension in the rope attached to the beam at \(C\) is double the tension in the rope attached to the beam at \(D\). The beam is modelled as a uniform rod, resting horizontally in equilibrium.
Find
  1. the tension in the rope attached to the beam at \(D\).
  2. the value of \(x\).
Edexcel M1 2023 October Q2
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{017cc2b0-9ec3-45ff-94c0-9d989badfd5d-04_677_1620_294_169} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Two fixed points, \(A\) and \(B\), are on a straight horizontal road.
The acceleration-time graph in Figure 2 represents the motion of a car travelling along the road as it moves from \(A\) to \(B\). At time \(t = 0\), the car passes through \(A\) with speed \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
At time \(t = 20 \mathrm {~s}\), the car passes through \(B\) with speed \(v \mathrm {~ms} ^ { - 1 }\)
  1. Show that \(v = 18\)
  2. Sketch a speed-time graph for the motion of the car from \(A\) to \(B\).
  3. Find the distance \(A B\).