Questions M1 - A-Level Maths

Find the time taken for the football to move from the point where it was kicked to the box.
Find the horizontal distance from the point where the football is kicked to the front of the box.
If the same student kicks the football at the same angle from the same initial position, what is the speed at which the student should kick the football if it is to hit the top back edge of the box?
Explain the significance of modelling the football as a particle in this context.
[0pt] [1 mark]
\includegraphics[max width=\textwidth, alt={}]{5dd17095-18a6-470b-a24a-4456c8e3ed31-23_2488_1709_219_153}
\section*{DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED}

Edexcel M1 Q1

A bee flies in a straight line from $A$ to $B$, where $\overrightarrow { A B } = \left( 3 \frac { 1 } { 2 } \mathbf { i } - 12 \mathbf { j } \right) \mathrm { m }$, in 5 seconds at a constant speed. Find
1. the straight-line distance $A B$,
2. the speed of the bee,
3. the velocity vector of the bee.
4. A small ball $B$, of mass 0.8 kg , is suspended from a horizontal ceiling by two light inextensible strings. $B$ is in equilibrium under gravity with both strings inclined at $30 ^ { \circ }$ to the horizontal, as shown.
  \includegraphics[max width=\textwidth, alt={}, center]{3e495748-ccb7-4c99-8387-160c4f0f9d4f-1_163_438_758_1480}
5. Find the tension, in N , in either string.
6. Calculate the magnitude of the least horizontal force that must be applied to $B$ in this position to cause one string to become slack.
7. A particle $P$ moves in a straight line through a fixed point $O$ with constant acceleration $a \mathrm {~ms} ^ { - 2 }$. 3 seconds after passing through $O , P$ is 6 m from $O$.
  After a further 6 seconds, $P$ has travelled a further 33 m in the same direction. Calculate
8. the value of $a$,
9. the speed with which $P$ passed through $O$.
10. A force of magnitude $F \mathrm {~N}$ is applied to a block of mass $M \mathrm {~kg}$ which is initially at rest on a horizontal plane. The block starts to move with acceleration $3 \mathrm {~ms} ^ { - 2 }$. Modelling the block as a particle,
  \includegraphics[max width=\textwidth, alt={}, center]{3e495748-ccb7-4c99-8387-160c4f0f9d4f-1_134_405_1672_1540}
11. if the plane is smooth, find an expression for $F$ in terms of $M$.
If the plane is rough, and the coefficient of friction between the block and the plane is $\mu$,
express $F$ in terms of $M , \mu$ and $g$.
Calculate the value of $\mu$ if $F = \frac { 1 } { 2 } M g$.

Edexcel M1 Q5

5. Two metal weights $A$ and $B$, of masses 2.4 kg and 1.8 kg respectively, are attached to the ends of a light inextensible string which passes over a smooth fixed pulley so that the string hangs vertically on each side. The system is released from rest with the string taut.

Calculate the acceleration of each weight and the tension in the string.
$A$ is now replaced by a different weight of mass $m \mathrm {~kg}$, where $m < 1 \cdot 8$, and the system is again released from rest. The magnitude of the acceleration has half of its previous value.
Calculate the value of $m$.
(6 marks) \section*{MECHANICS 1 (A)TEST PAPER 1 Page 2}

Edexcel M1 Q6

The diagram shows the speed-time graph for a particle during a period of $9 T$ seconds.
\includegraphics[max width=\textwidth, alt={}, center]{3e495748-ccb7-4c99-8387-160c4f0f9d4f-2_406_1162_319_351}
1. If $T = 5$, find
  1. the acceleration for each section of the motion,
  2. the total distance travelled by the particle.
2. Sketch, for this motion,
  1. an acceleration-time graph,
  2. a displacement-time graph.
3. Calculate the value of $T$ for which the distance travelled over the $9 T$ seconds is 3.708 km .
4. Two smooth spheres $A$ and $B$, of masses 60 grams and 90 grams respectively, are at rest on a smooth horizontal table. $A$ is projected towards $B$ with speed $4 \mathrm {~ms} ^ { - 1 }$ and the particles collide. After the collision, $A$ and $B$ move in the same direction as each other, with speeds $u \mathrm {~ms} ^ { - 1 }$ and $6 u \mathrm {~ms} ^ { - 1 }$ respectively. Calculate
5. the value of $u$,
6. the magnitude of the impulse exerted by $A$ on $B$, stating the units of your answer.
  (3 marks)
  $A$ and $B$ are now replaced in their original positions and projected towards each other with speeds $2 \mathrm {~ms} ^ { - 1 }$ and $8 \mathrm {~ms} ^ { - 1 }$ respectively. They collide again, after which $A$ moves with speed $7 \mathrm {~ms} ^ { - 1 }$, its direction of motion being reversed.
7. Find the speed of $B$ after this collision and state whether its direction of motion has been reversed.
8. In a theatre, three lights $A , B$ and $C$ are suspended from a horizontal beam $X Y$ of length $4.5 \mathrm {~m} . A$ and $C$ are each of mass 8 kg and $B$ is of mass 6 kg . The beam $X Y$ is held in place by vertical ropes $P X$ and $Q Y$, as shown.
  \includegraphics[max width=\textwidth, alt={}, center]{3e495748-ccb7-4c99-8387-160c4f0f9d4f-2_282_643_2104_1316}
In a simple mathematical model of this situation, $X Y$ is modelled as a light rod.
Calculate the tension in each of $P X$ and $Q Y$. In a refined model, $X Y$ is modelled as a uniform rod of mass $m \mathrm {~kg}$.
If the tension in $P X$ is 1.5 times that in $Q Y$, calculate the value of $m$.

Edexcel M1 Q1

A plank of wood $A B$, of mass 8 kg and length 6 m , rests on a support at $P$, where $A P = 4 \mathrm {~m}$. When particles of mass 1 kg and $k \mathrm {~kg}$ are suspended from $A$ and $B$ respectively, the plank rests horizontally in equilibrium.
Modelling the plank as a uniform rod, find
1. the value of $k$,
2. the magnitude of the force exerted by the support on the plank at $P$.
3. Forces of magnitude 4 N and 6 N act in directions which make an angle of $40 ^ { \circ }$ with each other, as shown. Calculate
  \includegraphics[max width=\textwidth, alt={}, center]{9c9b6087-d5a1-4fb0-b771-5ccc13a04bc4-1_209_478_840_1348}
4. the magnitude of the resultant of the two forces,
5. the angle, in degrees, between the resultant and the 4 N force.
6. A stone is dropped from rest at a height of 7 m above horizontal ground. It falls vertically, hits the ground and rebounds vertically upwards with half the speed with which it hit the ground. Calculate
7. the time taken for the stone to fall to the ground,
8. the speed with which the stone hits the ground,
9. the height to which the stone rises before it comes to instantaneous rest.
State two modelling assumptions that you have made.

Edexcel M1 Q4

4. A boy starts at the corner $O$ of a rectangular playing field and runs across the field with constant velocity vector $( \mathbf { i } + 2 \mathbf { j } ) \mathrm { ms } ^ { - 1 }$, where $\mathbf { i }$ and $\mathbf { j }$ are unit vectors in the directions of two perpendicular sides of the field. After 40 seconds, at the point $P$ in the field, he changes speed and direction so that his new velocity vector is $( 2 \cdot 4 \mathbf { i } - 1 \cdot 8 \mathbf { j } ) \mathrm { ms } ^ { - 1 }$ and maintains this velocity until he reaches the point $Q$, where $P Q = 75 \mathrm {~m}$.
Calculate (a) the distance $O P$,
(b) the time taken to travel from $P$ to $Q$,
(c) the position vector of $Q$ relative to $O$. Another boy travels directly from $O$ to $Q$ with constant velocity $( a \mathbf { i } + b \mathbf { j } ) \mathrm { ms } ^ { - 1 }$, leaving $O$ and reaching $Q$ at the same times as the first boy.
(d) Find the values of the constants $a$ and $b$. \section*{MECHANICS 1 (A)TEST PAPER 2 Page 2}

Edexcel M1 Q5

Two railway trucks $A$ and $B$, of masses 10000 kg and 7000 kg respectively, are moving towards each other along a horizontal straight track. The trucks collide, and in the collision $A$ exerts an impulse on $B$ of magnitude 84000 Ns. Immediately after the collision, the trucks move together with speed $10 \mathrm {~ms} ^ { - 1 }$. Modelling the trucks as particles,
1. find the speed of each truck immediately before the collision.
When the trucks are moving together along the track, the coefficient of friction between them and the track is 0.15 . Assuming that no other resisting forces act on the trucks, calculate
the magnitude of the resisting force on the trucks,
the time taken after the collision for the trucks to come to rest.

Edexcel M1 Q6

6. A small package $P$, of mass 1 kg , is initially at rest on the rough horizontal top surface of a wooden packing case which is 1.5 m long and 1 m high and stands on a horizontal floor. The coefficient of friction between $P$ and the case is 0.2 .
\includegraphics[max width=\textwidth, alt={}, center]{9c9b6087-d5a1-4fb0-b771-5ccc13a04bc4-2_287_517_941_1428}
$P$ is attached by a light inextensible string, which passes over a smooth fixed pulley, to a weight $Q$ of mass $M \mathrm {~kg}$ which rests against the smooth vertical side of the case.
The system is released from rest with $P 0.75 \mathrm {~m}$ from the pulley and $Q 0.5 \mathrm {~m}$ from the pulley. $P$ and $Q$ start to move with acceleration $0.4 \mathrm {~ms} ^ { - 2 }$. Calculate

the tension in the string, in N ,
the value of $M$,
the time taken for $Q$ to hit the floor. Given that $Q$ does not rebound from the floor,
calculate the distance of $P$ from the pulley when it comes to rest.

Edexcel M1 Q7

7. A car starts from rest at time $t = 0$ and moves along a straight road with constant acceleration 4 $\mathrm { ms } ^ { - 2 }$ for 10 seconds. It then travels at a constant speed for 50 seconds before decelerating to rest over a further distance of 240 m .

Sketch a graph of velocity against time for the total period of the car's motion.
Find the car's average speed for the whole journey. In reality the car's acceleration $a \mathrm {~ms} ^ { - 2 }$ in the first 10 seconds is not constant, but increases from 0 to $4 \mathrm {~ms} ^ { - 2 }$ in the first 5 seconds and then decreases to 0 again. A refined model designed to take account of this uses the formula $a = k \left( m t - t ^ { 2 } \right)$ for $0 \leq t \leq 10$.
Calculate the values of the constants $k$ and $m$.
Find the acceleration of the car when $t = 2$ according to this model.

Edexcel M1 Q1

A particle $P$, of mass 2.5 kg , initially at rest at the point $O$, moves on a smooth horizontal surface with constant acceleration $( \mathbf { i } + 2 \mathbf { j } ) \mathrm { ms } ^ { - 2 }$, where $\mathbf { i }$ and $\mathbf { j }$ are unit vectors in the directions due East and due North respectively. Find
1. the velocity vector of $P$ at time $t$ seconds after it leaves $O$,
2. the magnitude and direction of the velocity of $P$ when $t = 7$,
3. the magnitude, in N , of the force acting on $P$.
4. An iron bar $A B$, of length 4 m , is kept in a horizontal position by a support at $A$ and a wire attached to the point $P$ on the bar, where $P B = 0.85 \mathrm {~m}$. The bar is modelled as a non-uniform rod whose centre of mass is at $G$, where $A G = 1.4 \mathrm {~m}$, and the wire is modelled as a light inextensible string. Given that the tension in the wire is 12 N , calculate
5. the weight of the bar,
6. the magnitude of the reaction on the bar at $A$.
7. State briefly how you have used the given modelling assumption about the bar.
\includegraphics[max width=\textwidth, alt={}]{f8386a80-e428-43a7-acc8-f7ab11b2a53a-1_201_453_1399_378}
A small packet, of mass 1.2 kg , is at rest on a rough plane inclined at an angle $\alpha$ to the horizontal. The coefficient of friction between the packet and the plane is $\frac { 1 } { 8 }$.
When a force of magnitude 8.4 N , acting parallel to the plane, is applied to the packet as shown, the packet is just on the point of moving up the plane. Modelling the packet as a particle,
show that $7 ( \cos \alpha + 8 \sin \alpha ) = 40$. Given that the solution of this equation is $\alpha = 38 ^ { \circ }$,
find the acceleration with which the packet moves down the plane when it is released from rest with no external force applied.

Edexcel M1 Q4

4. A car moves in a straight line from $P$ to $Q$, a distance of 420 m , with constant acceleration. At $P$ the speed of the car is $8 \mathrm {~ms} ^ { - 1 }$. At $Q$ the speed of the car is $20 \mathrm {~ms} ^ { - 1 }$. Find

the time taken to travel from $P$ to $Q$,
the acceleration of the car,
the time taken for the car to travel 240 m from $P$. Given that the mass of the car is 1200 kg and the tractive force of the car is 900 N ,
find the magnitude of the resistance to the car's motion. \section*{MECHANICS 1 (A) TEST PAPER 3 Page 2}

Edexcel M1 Q5

Two smooth spheres $X$ and $Y$, of masses $x \mathrm {~kg}$ and $y \mathrm {~kg}$ respectively, are free to move in a smooth straight groove in a horizontal table. $X$ is projected with speed $6 \mathrm {~ms} ^ { - 1 }$ towards $Y$, which is stationary. After the collision $X$ moves with speed $2 \mathrm {~ms} ^ { - 1 }$ and $Y$ moves with speed $3 \mathrm {~ms} ^ { - 1 }$.
1. Calculate the two possible values of the ratio $x : y$.
2. State a modelling assumption that you have made concerning $X$ and $Y$.
  $Y$ now strikes a vertical barrier and rebounds along the groove with speed $k \mathrm {~ms} ^ { - 1 }$, colliding again with $X$ which is still moving at $2 \mathrm {~ms} ^ { - 1 }$. Given that in this impact $Y$ is brought to rest and the direction of motion of $X$ is reversed,
3. show that $k > 1 \cdot 5$.
4. Two particles $P$ and $Q$, of masses 3 kg and 2 kg respectively, rest on the smooth faces of a wedge whose cross-section is a triangle with angles $30 ^ { \circ } , 60 ^ { \circ }$ and $90 ^ { \circ }$, as shown. $P$ and $Q$ are connected by a light
  \includegraphics[max width=\textwidth, alt={}, center]{f8386a80-e428-43a7-acc8-f7ab11b2a53a-2_255_607_1078_1311}
  string, parallel to the lines of greatest slope of the two planes, which passes over a fixed pulley at the highest point of the wedge.
  The system is released from rest with $P 0.8 \mathrm {~m}$ from the pulley and $Q 1 \mathrm {~m}$ from the bottom of the wedge, and $Q$ starts to move down. Calculate
5. the acceleration of either particle,
6. the tension in the string,
7. the speed with which $P$ reaches the pulley.
Two modelling assumptions have been made about the string and the pulley.
State these two assumptions and briefly describe how you have used each one in your solution.

Edexcel M1 Q7

7. Two stones are projected simultaneously from a point $O$ on horizontal ground. Stone $A$ is thrown vertically upwards with speed $98 \mathrm {~ms} ^ { - 1 }$. Stone $B$ is projected along the smooth ground in a straight line at $24 \cdot 5 \mathrm {~ms} ^ { - 1 }$.

Find the distances of the two stones from $O$ after $t$ seconds, where $0 \leq t \leq 20$.
Show that the distance $d \mathrm {~m}$ between the two stones after $t$ seconds is given by $$d ^ { 2 } = 24 \cdot 01 \left( t ^ { 4 } - 40 t ^ { 3 } + 425 t ^ { 2 } \right) .$$
Hence find the range of values of $t$ for which the distance between the stones is decreasing.

Edexcel M1 Q1

A tennis ball, moving horizontally, hits a wall at $25 \mathrm {~ms} ^ { - 1 }$ and rebounds along the same straight line at $15 \mathrm {~ms} ^ { - 1 }$. The impulse exerted by the wall on the ball has magnitude 12 Ns .
1. Calculate the mass of the ball.
2. State any modelling assumptions that you have made.
\includegraphics[max width=\textwidth, alt={}]{977c24cc-8280-4881-8a62-65b7efd336ac-1_278_337_751_434}
Forces of magnitude $4 \mathrm {~N} , 5 \mathrm {~N}$ and 8 N act on a particle in directions whose bearings are $000 ^ { \circ } , 090 ^ { \circ }$ and $210 ^ { \circ }$ respectively. Find the magnitude of the resultant force and the bearing of the direction in which it acts.

Edexcel M1 Q3

3. A packing-case, of mass 60 kg , is standing on the floor of a lift. The mass of the lift-cage is 200 kg . The lift-cage is raised and lowered by means of a cable attached to its roof. In each of the following cases, find the magnitude of the force exerted by the floor of the liftcage on the packing-case and the tension in the cable supporting the lift:

The lift is descending with constant speed.
The lift is ascending and accelerating at $1.2 \mathrm {~ms} ^ { - 2 }$.
State any modelling assumptions you have made.

Edexcel M1 Q4

4. $A B$ is a light rod. Forces $\mathbf { F } , \mathbf { G }$ and $\mathbf { H }$, of magnitudes $3 \mathrm {~N} , 2 \mathrm {~N}$ and 6 N respectively, act upwards at right angles to the rod in a vertical plane at points dividing
\includegraphics[max width=\textwidth, alt={}, center]{977c24cc-8280-4881-8a62-65b7efd336ac-1_186_586_1741_1329}
$A B$ in the ratio $1 : 4 : 2 : 4$, as shown.
A single force $\mathbf { P }$ is applied downwards at the point $C$ to keep the rod horizontal in equilibrium.

State the magnitude of $\mathbf { P }$.
Show that $A C : C B = 5 : 6$. Two particles, of weights 3 N and $k \mathrm {~N}$, are now placed on the rod at $A$ and $B$ respectively, while the same upward forces $\mathbf { F } , \mathbf { G }$ and $\mathbf { H }$ act as before. It is found that a single downward force at the same point $C$ as before keeps $A B$ horizontal under gravity.
Find the value of $k$. \section*{MECHANICS 1 (A) TEST PAPER 4 Page 2}

Edexcel M1 Q5

Two smooth spheres $A$ and $B$, of masses $2 m$ and $m$ respectively, are connected by a light inextensible string which passes over a smooth fixed pulley as shown. $A$ is initially at rest on the rough horizontal surface of a table, the coefficient of friction between $A$
\includegraphics[max width=\textwidth, alt={}, center]{977c24cc-8280-4881-8a62-65b7efd336ac-2_253_323_255_1622}
and the table being $\frac { 2 } { 7 }$. $B$ hangs freely on the end of the vertical portion of the string. $A$ is now given an impulse, directed away from the pulley, of magnitude 5 m Ns.
1. Show that the system starts to move with speed $2.5 \mathrm {~ms} ^ { - 1 }$.
2. State which modelling assumption ensures that the tensions in the two sections of the string can be taken to be equal.
Given that $A$ comes to rest before it reaches the edge of the table and before $B$ hits the pulley,
find the time taken for the system to come to rest.
Find the distance travelled by $A$ before it first comes to rest.

Edexcel M1 Q6

6. The diagram shows the velocity-time graph for a cyclist's journey. Each section has constant acceleration or deceleration and the three sections are of equal duration $x$ seconds each.
Given that the total distance travelled is 792 m ,
\includegraphics[max width=\textwidth, alt={}, center]{977c24cc-8280-4881-8a62-65b7efd336ac-2_337_647_1128_1284}

find the value of $x$ and the acceleration for the first section of the journey. Another cyclist covers the same journey in three sections of equal duration, accelerating at $\frac { 1 } { 11 } \mathrm {~ms} ^ { - 2 }$ for the first section, travelling at constant speed for the second section and decelerating at $\frac { 1 } { 11 } \mathrm {~ms} ^ { - 2 }$ for the third section.
Find the time taken by this cyclist to complete the journey.
Show that the maximum speeds of both cyclists are the same.

Edexcel M1 Q7

7. Relative to a fixed origin $O$, the points $X$ and $Y$ have position vectors $( 4 \mathbf { i } - 5 \mathbf { j } ) \mathrm { m }$ and $( 12 \mathbf { i } + \mathbf { j } ) \mathbf { m }$ respectively, where $\mathbf { i }$ and $\mathbf { j }$ are perpendicular unit vectors.

Find the distance $X Y$. A particle $P$ of mass 2 kg moves from $X$ to $Y$ in 4 seconds, in a straight line at a constant speed.
Show that the velocity vector of $P$ is $( 2 \mathbf { i } + 1 \cdot 5 \mathbf { j } ) \mathrm { ms } ^ { - 1 }$. The particle continues beyond $Y$ with the same constant velocity.
Write down an expression for the position vector of $P t$ seconds after leaving $X$.
Find the value of $t$ when $P$ is at the point with position vector $( 16 \mathbf { i } + 4 \mathbf { j } ) \mathrm { m }$. When it is moving with the same constant speed, $P$ collides directly with another particle $Q$, of mass 4 kg , which is at rest. $P$ and $Q$ coalesce and move together as a single particle.
Find the velocity vector of the combined particle after the collision.
(5 marks)

Edexcel M1 Q1

Two forces, both of magnitude 5 N , act on a particle in the directions with bearings $000 ^ { \circ }$ and $070 ^ { \circ }$, as shown. Calculate
1. the magnitude of the resultant force on the particle,
2. the bearing on which this resultant force acts.
3. A uniform plank $X Y$ has length 7 m and mass 2 kg . It is placed with the portion $Z Y$ in contact with a
  \includegraphics[max width=\textwidth, alt={}, center]{38e355b0-9d75-40ad-b450-bd74c5135c7f-1_149_616_843_1334}
  horizontal surface, where $Z Y = 2.8 \mathrm {~m}$. To prevent the
  \includegraphics[max width=\textwidth, alt={}, center]{38e355b0-9d75-40ad-b450-bd74c5135c7f-1_207_253_404_1505}
\section*{MECHANICS 1 (A) TEST PAPER 5 Page 2}

Edexcel M1 Q5

$\mathbf { i }$ and $\mathbf { j }$ are perpendicular unit vectors. The point $A$ has position vector $6 \mathbf { j } \mathrm {~m}$ relative to an origin $O$. At time $t = 0$ a particle $P$ starts from $O$ and moves with constant velocity ( $5 \mathbf { i } + 2 \mathbf { j }$ ) $\mathrm { ms } ^ { - 1 }$. At the same instant a particle $Q$ starts from $A$ and moves with constant velocity $4 \mathrm { ims } ^ { - 1 }$.
1. Write down the position vectors of $P$ and of $Q$ at time $t$ seconds.
2. Show that the distance $d \mathrm {~m}$ between $P$ and $Q$ at time $t$ seconds is such that
$$d ^ { 2 } = 5 t ^ { 2 } - 24 t + 36 .$$
Find the value of $t$ for which $d ^ { 2 }$ is a minimum.
Hence find the minimum distance between $P$ and $Q$, and state the position vector of each particle when they are closest together.

Edexcel M1 Q6

6. $A , B$ and $C$ are three small spheres of equal radii and masses $2 m , m$ and $5 m$ respectively. They are placed in a straight line on a smooth horizontal surface. $A$ is projected with speed $6 \mathrm {~ms} ^ { - 1 }$ towards $B$, which is at rest. When $A$ hits $B$ it exerts an impulse of magnitude 8 m Ns on $B$.

Find the speed with which $B$ starts to move.
Show that the speed of $A$ after it collides with $B$ is $2 \mathrm {~ms} ^ { - 1 }$. After travelling $3 \mathrm {~m} , B$ hits $C$, which is then travelling towards $B$ at $2 \cdot 2 \mathrm {~ms} ^ { - 1 } . C$ is brought to rest by this impact.
Show that the direction of $B$ 's motion is reversed and find its new speed.
Find how far $B$ now travels before it collides with $A$ again.
State a modelling assumption that you have made about the spheres.

Edexcel M1 Q7

7. A particle $P$, of mass $m$, is in contact with a rough plane inclined at $30 ^ { \circ }$ to the horizontal as shown. A light string is attached to $P$ and makes an angle of $30 ^ { \circ }$ with the plane. When the tension in this string has magnitude $k m g , P$ is
\includegraphics[max width=\textwidth, alt={}, center]{38e355b0-9d75-40ad-b450-bd74c5135c7f-2_268_474_1759_1407}
just on the point of moving up the plane.

Show that $\mu$, the coefficient of friction between $P$ and the plane, is $\frac { k \sqrt { } 3 - 1 } { \sqrt { } 3 - k }$.
Given further that $k = \frac { 3 \sqrt { } 3 } { 7 }$, deduce that $\mu = \frac { \sqrt { } 3 } { 6 }$. The string is now removed.
Determine whether $P$ will move down the plane and, if it does, find its acceleration.
Give a reason why the way in which $P$ is shown in the diagram might not be consistent with the modelling assumptions that have been made.

Edexcel M1 Q1

1.
\includegraphics[max width=\textwidth, alt={}, center]{31efa627-5114-4797-9d46-7f1311c18ff8-1_490_254_354_347} A vertical pole $X Y$, of length 2.5 m and mass 0.5 kg , has its lower end $Y$ free to move in a smooth horizontal groove. Forces of magnitude 0.2 N and 0.14 N are applied to the pole horizontally at the points $V$ and $W$ respectively, where $X V = 1.5 \mathrm {~m}$ and $V W = 0.5 \mathrm {~m}$.
Find, to the nearest cm , the distance from $X$ at which an opposing horizontal force must be applied to keep the pole at rest in equilibrium, and state the magnitude of this force.

Edexcel M1 Q2

2. A particle passes through a point $O$ with speed $9 \mathrm {~ms} ^ { - 1 }$ and moves in a straight line with constant acceleration $3.6 \mathrm {~ms} ^ { - 2 }$ for $t$ seconds until it reaches the point $P$. The acceleration is then reduced to $2 \mathrm {~ms} ^ { - 2 }$ and this is maintained for another $t$ seconds until the particle passes the point $Q$ with speed $16 \mathrm {~ms} ^ { - 1 }$. Calculate

the time taken by the particle to travel from $O$ to $Q$,
the distance $O Q$.

Questions M1 (1912 questions)

Browse by module

Browse by board

AQA M1 2016 June Q7

Edexcel M1 Q1

Edexcel M1 Q5

Edexcel M1 Q6

Edexcel M1 Q1

Edexcel M1 Q4

Edexcel M1 Q5

Edexcel M1 Q6

Edexcel M1 Q7

Edexcel M1 Q1

Edexcel M1 Q4

Edexcel M1 Q5

Edexcel M1 Q7

Edexcel M1 Q1

Edexcel M1 Q3

Edexcel M1 Q4

Edexcel M1 Q5

Edexcel M1 Q6

Edexcel M1 Q7

Edexcel M1 Q1

Edexcel M1 Q5

Edexcel M1 Q6

Edexcel M1 Q7

Edexcel M1 Q1

Edexcel M1 Q2