Legacy M1 — Mechanics 1: Edexcel A‑Level Maths questions

Edexcel A-Level Maths past-paper questions on L.M1 Legacy M1 — Mechanics 1, 2010–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 112 questions on Legacy M1 — Mechanics 1, as a list

June 2018, Legacy M1, Q1 (6 marks): Two particles, P and Q, have masses 3m and m respectively. They are moving in opposite directions towards each other along the same straight line on a smooth ho
June 2018, Legacy M1, Q2 (10 marks): 30° P newtons 20° Figure 1 A particle of mass 2 kg lies on a rough plane. The plane is inclined to the horizontal at 30°. The coefficient of friction between th
June 2018, Legacy M1, Q3 (7 marks): A P D B 9 m 1.5 m 3.5 m C 3 m Figure 2 A wooden beam AB, of mass 150 kg and length 9 m, rests in a horizontal position supported by two vertical ropes. The rope
June 2018, Legacy M1, Q4 (13 marks): A ball of mass 0.2 kg is projected vertically downwards with speed U m s–1 from a point A which is 2.5 m above horizontal ground. The ball hits the ground. Imme
June 2018, Legacy M1, Q5 (10 marks): Figure 3 A lift of mass 250 kg is being raised by a vertical cable attached to the top of the lift. A woman of mass 60 kg stands on the horizontal floor inside
June 2018, Legacy M1, Q6 (13 marks): [In this question i and j are horizontal unit vectors due east and due north respectively] Two forces F1 and F2 act on a particle P of mass 0.5 kg. F1 = (4i – 6
June 2018, Legacy M1, Q7 (16 marks): d Q(m) P(4m) h X Į Figure 4 A particle P of mass 4m is held at rest at the point X on the surface of a rough inclined plane which is fixed to horizontal ground.
June 2017, Legacy M1, Q1 (6 marks): Three forces, (15i + j) N, (5qi – pj) N and (–3pi – qj) N, where p and q are constants, act on a particle. Given that the particle is in equilibrium, find the v
June 2017, Legacy M1, Q2 (7 marks): Two particles, P and Q, have masses 2m and 3m respectively. They are moving towards each other in opposite directions on a smooth horizontal plane when they col
June 2017, Legacy M1, Q3 (9 marks): A plank AB has length 6m and mass 30kg. The point C is on the plank with CB = 2m. The plank rests in equilibrium in a horizontal position on supports at A and C
June 2017, Legacy M1, Q4 (9 marks): 10N Į Figure 1 A particle P of mass 5kg is held at rest in equilibrium on a rough inclined plane by a horizontal force of magnitude 10N. The plane is inclined t
June 2017, Legacy M1, Q5 (6 marks): P Q (0.75kg) (0.5kg) Figure 2 A vertical light rod PQ has a particle of mass 0.5kg attached to it at P and a particle of mass 0.75kg attached to it at Q, to for
June 2017, Legacy M1, Q6 (9 marks): A cyclist is moving along a straight horizontal road and passes a point A. Five seconds later, at the instant when she is moving with speed 10 ms–1, she passes
June 2017, Legacy M1, Q7 (14 marks): [In this question i and j are horizontal unit vectors due east and due north respectively and position vectors are given relative to a fixed origin O.] Two ship
June 2017, Legacy M1, Q8 (15 marks): d P A(2m) B(m) h Figure 3 Two particles, A and B, have masses 2m and m respectively. The particles are attached to the ends of a light inextensible string. Part
June 2016, Legacy M1, Q1 (10 marks): [In this question i and j are horizontal unit vectors due east and due north respectively and position vectors are given relative to a fixed origin O.] Two cars
June 2016, Legacy M1, Q2 (6 marks): A B Figure 1 A vertical rope AB has its end B attached to the top of a scale pan. The scale pan has mass 0.5 kg and carries a brick of mass 1.5 kg, as shown in
June 2016, Legacy M1, Q3 (7 marks): A particle P of mass 0.4 kg is moving on rough horizontal ground when it hits a fixed vertical plane wall. Immediately before hitting the wall, P is moving with
June 2016, Legacy M1, Q4 (12 marks): Two trains M and N are moving in the same direction along parallel straight horizontal tracks. At time t = 0, M overtakes N whilst they are travelling with spee
June 2016, Legacy M1, Q5 (10 marks): 40 N 30° 20° P (2 kg) Figure 2 A particle P of mass 2 kg is held at rest in equilibrium on a rough plane by a constant force of magnitude 40 N. The direction of
June 2016, Legacy M1, Q6 (7 marks): A non-uniform plank AB has length 6 m and mass 30 kg. The plank rests in equilibrium in a horizontal position on supports at the points S and T of the plank whe
June 2016, Legacy M1, Q7 (11 marks): Two forces F1 and F2 act on a particle P. The force F1 is given by F1 = (–i + 2j) N and F2 acts in the direction of the vector (i + j). Given that the resultant
June 2016, Legacy M1, Q8 (12 marks): P (1.5 kg) Q (3 kg) Figure 3 Two particles P and Q have masses 1.5 kg and 3 kg respectively. The particles are attached to the ends of a light inextensible stri
June 2015, Legacy M1, Q1 (6 marks): Particle P of mass m and particle Q of mass km are moving in opposite directions on a smooth horizontal plane when they collide directly. Immediately before the
June 2015, Legacy M1, Q2 (7 marks): A small stone is projected vertically upwards from a point O with a speed of 19.6msí1. Modelling the stone as a particle moving freely under gravity, (a) find t
June 2015, Legacy M1, Q3 (7 marks): Figure 1 A particle of mass 2 kg is suspended from a horizontal ceiling by two light inextensible strings, PR and QR. The particle hangs at R in equilibrium, wi
June 2015, Legacy M1, Q4 (7 marks): Figure 2 A lift of mass 200 kg is being lowered into a mineshaft by a vertical cable attached WRWKHWRSRIWKHOLIW$FUDWHRIPDVVNJLVRQWKHÀRRULQVL
June 2015, Legacy M1, Q5 (12 marks): Figure 3 A beam AB has length 5 m and mass 25 kg. The beam is suspended in equilibrium in a horizontal position by two vertical ropes. One rope is attached to t
June 2015, Legacy M1, Q6 (8 marks): A particle P is moving with constant velocity. The position vector of P at time t seconds (t .0) is r metres, relative to a fixed origin O, and is given by r =
June 2015, Legacy M1, Q7 (13 marks): 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 0.5 m sí2
June 2015, Legacy M1, Q8 (15 marks): Figure 4 Two particles P and Q have mass 4 kg and 0.5 kg respectively. The particles are attached to the ends of a light inextensible string. Particle P is held
June 2014, Legacy M1, Q1 (6 marks): Figure 1 A particle of weight W newtons is attached at C to two light inextensible strings AC and BC. The other ends of the strings are attached to fixed points
June 2014, Legacy M1, Q2 (7 marks): Figure 2 A rough plane is inclined at 40° to the horizontal. Two points A and B are 3 metres apart and lie on a line of greatest slope of the inclined plane, wi
June 2014, Legacy M1, Q3 (13 marks): A ball of mass 0.3 kg is released from rest at a point which is 2 m above horizontal ground. The ball moves freely under gravity. After striking the ground, the
June 2014, Legacy M1, Q4 (12 marks): Figure 3 A beam AB has weight W newtons and length 4 m. The beam is held in equilibrium in a horizontal position by two vertical ropes attached to the beam. One
June 2014, Legacy M1, Q5 (12 marks): A particle P of mass 0.5 kg is moving under the action of a single force (3i – 2j) N. (a) Show that the magnitude of the acceleration of P is 2 13 m s–2. (4) At
June 2014, Legacy M1, Q6 (9 marks): Figure 4 Two forces P and Q act on a particle at O. The angle between the lines of action of P and Q is 120° as shown in Figure 4. The force P has magnitude 20
June 2014, Legacy M1, Q7 (16 marks): Figure 5 Three particles A, B and C have masses 3m, 2m and 2m respectively. Particle C is attached to particle B. Particles A and B are connected by a light ine
June 2014, Legacy M1 (01R), Q1 (6 marks): Figure 1 A particle P of weight W newtons is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point O. A h
June 2014, Legacy M1 (01R), Q2 (10 marks): Two forces (4i – 2j) N and (2i + qj) N act on a particle P of mass 1.5 kg. The resultant of these two forces is parallel to the vector (2i + j). (a) Find the va
June 2014, Legacy M1 (01R), Q3 (13 marks): A car starts from rest and moves with constant acceleration along a straight horizontal road. The car reaches a speed of V m s–1 in 20 seconds. It moves at cons
June 2014, Legacy M1 (01R), Q4 (8 marks): At time t = 0, a particle is projected vertically upwards with speed u from a point A. The particle moves freely under gravity. At time T the particle is at its
June 2014, Legacy M1 (01R), Q5 (14 marks): Figure 2 Two particles A and B have masses 2m and 3m respectively. The particles are connected by a light inextensible string which passes over a smooth light f
June 2014, Legacy M1 (01R), Q6 (11 marks): Figure 3 A non-uniform beam AD has weight W newtons and length 4 m. It is held in equilibrium in a horizontal position by two vertical ropes attached to the bea
June 2014, Legacy M1 (01R), Q7 (13 marks): Figure 4 A particle P of mass 2.7 kg lies on a rough plane inclined at 40° to the horizontal. The particle is held in equilibrium by a force of magnitude 15 N a
June 2013, Legacy M1, Q1 (6 marks): Particle P has mass 3 kg and particle Q has mass m kg. The particles are moving in opposite directions along a smooth horizontal plane when they collide directl
June 2013, Legacy M1, Q2 (6 marks): A woman travels in a lift. The mass of the woman is 50 kg and the mass of the lift is 950 kg. The lift is being raised vertically by a vertical cable which is a
June 2013, Legacy M1, Q3 (8 marks): 30° 2 kg Figure 1 A box of mass 2 kg is held in equilibrium on a fixed rough inclined plane by a rope. The rope lies in a vertical plane containing a line of
June 2013, Legacy M1, Q4 (9 marks): A lorry is moving along a straight horizontal road with constant acceleration. The lorry passes a point A with speed u m s–1, (u < 34), and 10 seconds later pas
June 2013, Legacy M1, Q5 (11 marks): A car is travelling along a straight horizontal road. The car takes 120 s to travel between two sets of traffic lights which are 2145 m apart. The car starts fr
June 2013, Legacy M1, Q6 (14 marks): A beam AB has length 15 m. The beam rests horizontally in equilibrium on two smooth supports at the points P and Q, where AP = 2 m and QB = 3 m. When a child of
June 2013, Legacy M1, Q7 (11 marks): [In this question, the horizontal unit vectors i and j are directed due east and due north respectively.] The velocity, v m s–1, of a particle P at time t secon
June 2013, Legacy M1, Q8 (10 marks): A (2m) B (3m) Figure 2 Two particles A and B have masses 2m and 3m respectively. The particles are attached to the ends of a light inextensible string. Particle
June 2013, Legacy M1 (01R), Q1 (6 marks): Two particles A and B, of mass 2 kg and 3 kg respectively, are moving towards each other in opposite directions along the same straight line on a smooth horizon
June 2013, Legacy M1 (01R), Q2 (8 marks): Figure 1 A particle of weight 8 N is attached at C to the ends of two light inextensible strings AC and BC. The other ends, A and B, are attached to a fixed hor
June 2013, Legacy M1 (01R), Q3 (9 marks): Figure 2 A fixed rough plane is inclined at 30° to the horizontal. A small smooth pulley P is fixed at the top of the plane. Two particles A and B, of mass 2 kg
June 2013, Legacy M1 (01R), Q4 (7 marks): At time t = 0, two balls A and B are projected vertically upwards. The ball A is projected vertically upwards with speed 2 m s–1 from a point 50 m above the hor
June 2013, Legacy M1 (01R), Q5 (10 marks): Figure 3 A particle P of mass 0.6 kg slides with constant acceleration down a line of greatest slope of a rough plane, which is inclined at 25° to the horizonta
June 2013, Legacy M1 (01R), Q6 (11 marks): [In this question i and j are horizontal unit vectors due east and due north respectively. Position vectors are given with respect to a fixed origin O.] A ship
June 2013, Legacy M1 (01R), Q7 (11 marks): Figure 4 A truck of mass 1750 kg is towing a car of mass 750 kg along a straight horizontal road. The two vehicles are joined by a light towbar which is incline
June 2013, Legacy M1 (01R), Q8 (13 marks): Figure 5 A uniform rod AB has length 2 m and mass 50 kg. The rod is in equilibrium in a horizontal position, resting on two smooth supports at C and D, where AC
January 2013, Legacy M1, Q1 (7 marks): Two particles P and Q have masses 4m and m respectively. The particles are moving towards each other on a smooth horizontal plane and collide directly. The spee
January 2013, Legacy M1, Q2 (9 marks): A steel girder AB, of mass 200 kg and length 12 m, rests horizontally in equilibrium on two smooth supports at C and at D, where AC = 2 m and DB = 2 m. A man of
January 2013, Legacy M1, Q3 (8 marks): A particle P of mass 2 kg is attached to one end of a light string, the other end of which is attached to a fixed point O. The particle is held in equilibrium,
January 2013, Legacy M1, Q4 (9 marks): A lifeboat slides down a straight ramp inclined at an angle of 15º to the horizontal. The lifeboat has mass 800 kg and the length of the ramp is 50 m. The lifeb
January 2013, Legacy M1, Q5 (15 marks): 30 1 (m s ) v − O T t (s) Figure 4 The velocity-time graph in Figure 4 represents the journey of a train P travelling along a straight horizontal track between
January 2013, Legacy M1, Q6 (11 marks): [In this question, i and j are horizontal unit vectors due east and due north respectively and position vectors are given with respect to a fixed origin.] A shi
January 2013, Legacy M1, Q7 (16 marks): P A (2m) X B (4m) h Figure 5 Figure 5 shows two particles A and B, of mass 2m and 4m respectively, connected by a light inextensible string. Initially A is he
June 2012, Legacy M1, Q1 (6 marks): Two particles A and B, of mass 5m kg and 2m kg respectively, are moving in opposite directions along the same straight horizontal line. The particles collide di
June 2012, Legacy M1, Q2 (7 marks): A P Q B G 3 m 0.8 m 0.6 m Figure 1 A non-uniform rod AB has length 3 m and mass 4.5 kg. The rod rests in equilibrium, in a horizontal position, on two smooth su
June 2012, Legacy M1, Q3 (9 marks): 20 N 30° Figure 2 A box of mass 5 kg lies on a rough plane inclined at 30° to the horizontal. The box is held in equilibrium by a horizontal force of magnitude
June 2012, Legacy M1, Q4 (13 marks): A car is moving on a straight horizontal road. At time t = 0, the car is moving with speed 20 m s–1 and is at the point A. The car maintains the speed of 20 m s
June 2012, Legacy M1, Q5 (12 marks): A particle P is projected vertically upwards from a point A with speed u m s–1. The point A is 17.5 m above horizontal ground. The particle P moves freely under
June 2012, Legacy M1, Q6 (13 marks): [In this question i and j are horizontal unit vectors due east and due north respectively and position vectors are given with respect to a fixed origin.] A ship
June 2012, Legacy M1, Q7 (15 marks): P(0.3 kg) Q(0.5 kg) F(4 N) Figure 3 Two particles P and Q, of mass 0.3 kg and 0.5 kg respectively, are joined by a light horizontal rod. The system of the parti
January 2012, Legacy M1, Q1 (5 marks): A railway truck P, of mass m kg, is moving along a straight horizontal track with speed 15 m s–1. Truck P collides with a truck Q of mass 3000 kg, which is at r
January 2012, Legacy M1, Q2 (6 marks): A car of mass 1000 kg is towing a caravan of mass 750 kg along a straight horizontal road. The caravan is connected to the car by a tow-bar which is parallel to
January 2012, Legacy M1, Q3 (8 marks): Three forces F1, F2 and F3 acting on a particle P are given by F1 = (7i – 9j) N F2 = (5i + 6j) N F3 = (pi + qj) N where p and q are constants. Given that P is i
January 2012, Legacy M1, Q4 (9 marks): d d 5d A C G B D Figure 1 A non-uniform rod AB, of mass m and length 5d, rests horizontally in equilibrium on two supports at C and D, where AC = DB = d, as sho
January 2012, Legacy M1, Q5 (11 marks): A stone is projected vertically upwards from a point A with speed u m s–1. After projection the stone moves freely under gravity until it returns to A. The time
January 2012, Legacy M1, Q6 (13 marks): A car moves along a straight horizontal road from a point A to a point B, where AB = 885 m. The car accelerates from rest at A to a speed of 15 m s–1 at a const
January 2012, Legacy M1, Q7 (9 marks): [In this question, the unit vectors i and j are due east and due north respectively. Position vectors are relative to a fixed origin O.] A boat P is moving with
January 2012, Legacy M1, Q8 (14 marks): 30° P 30° 36 N Figure 2 A particle P of mass 4 kg is moving up a fixed rough plane at a constant speed of 16 m s–1 under the action of a force of magnitude 36 N
June 2011, Legacy M1, Q1 (8 marks): At time t = 0 a ball is projected vertically upwards from a point O and rises to a maximum height of 40 m above O. The ball is modelled as a particle moving fre
June 2011, Legacy M1, Q2 (8 marks): Particle P has mass 3 kg and particle Q has mass 2 kg. The particles are moving in opposite directions on a smooth horizontal plane when they collide directly.
June 2011, Legacy M1, Q3 (9 marks): 4 N α Figure 1 A particle of weight W newtons is held in equilibrium on a rough inclined plane by a horizontal force of magnitude 4 N. The force acts in a verti
June 2011, Legacy M1, Q4 (12 marks): A girl runs a 400 m race in a time of 84 s. In a model of this race, it is assumed that, starting from rest, she moves with constant acceleration for 4 s, reach
June 2011, Legacy M1, Q5 (11 marks): A plank PQR, of length 8 m and mass 20 kg, is in equilibrium in a horizontal position on two supports at P and Q, where PQ = 6 m. A child of mass 40 kg stands o
June 2011, Legacy M1, Q6 (16 marks): Q P Figure 2 Two particles P and Q have masses 0.3 kg and m kg respectively. The particles are attached to the ends of a light inextensible string. The string p
June 2011, Legacy M1, Q7 (11 marks): [In this question i and j are unit vectors due east and due north respectively. Position vectors are given relative to a fixed origin O.] Two ships P and Q are
January 2011, Legacy M1, Q1 (5 marks): Two particles B and C have mass m kg and 3 kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table. The two part
January 2011, Legacy M1, Q2 (8 marks): A ball is thrown vertically upwards with speed u m s 1 − from a point P at height h metres above the ground. The ball hits the ground 0.75 s later. The speed of
January 2011, Legacy M1, Q3 (10 marks): Figure 1 A uniform beam AB has mass 20 kg and length 6 m. The beam rests in equilibrium in a horizontal position on two smooth supports. One support is at C, wh
January 2011, Legacy M1, Q4 (11 marks): A particle P of mass 2 kg is moving under the action of a constant force F newtons. The velocity of P is 1 (2 5 ) m s− − i j at time 0, = t and 1 (7 10 ) m s− +
January 2011, Legacy M1, Q5 (10 marks): A car accelerates uniformly from rest for 20 seconds. It moves at constant speed v m s 1 s− for the next 40 seconds and then decelerates uniformly for 10 second
January 2011, Legacy M1, Q6 (15 marks): α 120 N 30 N Figure 2 A particle of weight 120 N is placed on a fixed rough plane which is inclined at an angle D to the horizontal, where tan . D = 3 4 The coe
January 2011, Legacy M1, Q7 (16 marks): A B P 7kg 3kg θ Figure 4 Two particles A and B, of mass 7 kg and 3 kg respectively, are attached to the ends of a light inextensible string. Initially B is held
June 2010, Legacy M1, Q1 (5 marks): A particle P is moving with constant velocity 1 ( 3 2 ) m s . − − + i j At time 6 s t = P is at the point with position vector ( 4 7 ) m. − − i j Find the dista
June 2010, Legacy M1, Q2 (7 marks): Particle P has mass kg m and particle Q has mass 3 kg. m The particles are moving in opposite directions along a smooth horizontal plane when they collide direc
June 2010, Legacy M1, Q3 (7 marks): 100 N 30° Figure 1 A small box is pushed along a floor. The floor is modelled as a rough horizontal plane and the box is modelled as a particle. The coefficient
June 2010, Legacy M1, Q4 (7 marks): A beam AB has length 6 m and weight 200 N. The beam rests in a horizontal position on two supports at the points C and D, where 1 m AC = and 1 m. DB = Two child
June 2010, Legacy M1, Q5 (12 marks): Two cars P and Q are moving in the same direction along the same straight horizontal road. Car P is moving with constant speed 1 25 m s . − At time 0, t = P ove
June 2010, Legacy M1, Q6 (10 marks): A ball is projected vertically upwards with a speed of 1 14.7 m s− from a point which is 49 m above horizontal ground. Modelling the ball as a particle moving f
June 2010, Legacy M1, Q7 (10 marks): α N P Figure 2 A particle of mass 0.4 kg is held at rest on a fixed rough plane by a horizontal force of magnitude P newtons. The force acts in the vertical pla
June 2010, Legacy M1, Q8 (17 marks): A B 1m 1m Figure 3 Two particles A and B have mass 0.4 kg and 0.3 kg respectively. The particles are attached to the ends of a light inextensible string. The st
January 2010, Legacy M1, Q1 (6 marks): A particle A of mass 2 kg is moving along a straight horizontal line with speed 12 m s–1. Another particle B of mass m kg is moving along the same straight line
January 2010, Legacy M1, Q2 (8 marks): An athlete runs along a straight road. She starts from rest and moves with constant acceleration for 5 seconds, reaching a speed of 8 m s–1. This speed is then
January 2010, Legacy M1, Q3 (8 marks): Figure 1 A particle of mass m kg is attached at C to two light inextensible strings AC and BC. The other ends of the strings are attached to fixed points A and
January 2010, Legacy M1, Q4 (10 marks): Figure 2 A pole AB has length 3 m and weight W newtons. The pole is held in a horizontal position in equilibrium by two vertical ropes attached to the pole at t
January 2010, Legacy M1, Q5 (15 marks): A particle of mass 0.8 kg is held at rest on a rough plane. The plane is inclined at 30° to the horizontal. The particle is released from rest and slides down a
January 2010, Legacy M1, Q6 (14 marks): Figure 4 Two particles A and B have masses 5m and km respectively, where k < 5. The particles are connected by a light inextensible string which passes over a s
January 2010, Legacy M1, Q7 (14 marks): [In this question, i and j are horizontal unit vectors due east and due north respectively and position vectors are given with respect to a fixed origin.] A shi

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