Edexcel IAL M1 June 2023 mark scheme and question paper (WME01/01)

3 M1 questions like these, with worked solutions

Written and checked by us, not taken from the Pearson paper. Try each one, then tap "Worked solution" to see every step and its marks.

1. Kinematics · 5 marks

   A particle moving with constant acceleration passes three points $A$, $B$ and $C$, in that order, on a straight line. The distance $AB$ is $20\text{ m}$ and the distance $AC$ is $84\text{ m}$. The speed of the particle at $B$ is $12{\text{ m s}}^{-1}$ and its speed at $C$ is $20{\text{ m s}}^{-1}$. Find the acceleration of the particle and its speed at $A$.

   Worked solution

   1. M1 for $BC=84-20=64\text{ m}$.
   2. M1 for $v^2=u^2+2as$ from $B$ to $C$: ${20}^2={12}^2+2a(64)$.
   3. A1 for $128a=256\Rightarrow a=2{\text{ m s}}^{-2}$.
   4. M1 for $v^2=u^2+2as$ from $A$ to $B$: ${12}^2=u_A^2+2(2)(20)$.
   5. A1 for $u_A^2=64\Rightarrow u_A=8{\text{ m s}}^{-1}$.

2. Vectors (Mechanics context) · 7 marks

   At time $t$ hours after 09:00, a boat $P$ has position vector $((1+2t)\mathbf{i}+(5-t)\mathbf{j})$ km relative to a fixed origin. A lighthouse $L$ is at the point with position vector $(8\mathbf{i}+7\mathbf{j})$ km.

   (a) Find $\overrightarrow{PL}$ in terms of $t$. [2]

   (b) Show that $P{L}^2=5t^2-24t+53$. [2]

   (c) Find the shortest distance between the boat and the lighthouse, and the time at which it occurs. [3]

   Worked solution

   (a) $\overrightarrow{PL}=(8\mathbf{i}+7\mathbf{j})-((1+2t)\mathbf{i}+(5-t)\mathbf{j})$ M1

   $(7-2t)\mathbf{i}+(2+t)\mathbf{j}$ A1

   (b) $P{L}^2=(7-2t{)}^2+(2+t{)}^2$ M1

   $=49-28t+4t^2+4+4t+t^2=5t^2-24t+53$ A1 (cso)

   (c) $5t^2-24t+53=5(t-2.4{)}^2+24.2$ (or any complete method for the minimum) M1

   $t=2.4$, i.e. 11:24 A1

   Shortest distance $\sqrt{24.2}=4.92$ km A1

3. Momentum and Impulse · 4 marks

   A ball of mass $0.5\text{ kg}$ is dropped from rest from a height of $19.6\text{ m}$ above horizontal ground. It rebounds to a height of $4.9\text{ m}$. Calculate the magnitude of the impulse exerted by the ground on the ball. (Take $g=9.8{\text{ m s}}^{-2}$)

   Worked solution

   1. M1 for finding the velocity just before impact using $v^2=u^2+2as$: $v_1^2=0+2(9.8)(19.6)={19.6}^2⟹v_1=19.6{\text{ m s}}^{-1}$ downwards.
   2. M1 for finding the velocity just after impact using $v^2=u^2+2as$: $0=v_2^2-2(9.8)(4.9)⟹v_2^2={9.8}^2⟹v_2=9.8{\text{ m s}}^{-1}$ upwards.
   3. M1 for calculating the impulse: $I=m(v_2-v_1)=0.5(9.8-(-19.6))$.
   4. A1 for evaluating $I=0.5(29.4)=14.7\text{ N s}$.

More on these topics: Kinematics · Vectors (Mechanics context) · Momentum and Impulse

What's on this paper

What this paper is like

• Shape: 8 questions, 75 marks in 1 h 30 min (about 1.2 minutes a mark); questions from 7 to 12 marks.
• Biggest question: Q4, 12 marks: beam suspended by two ropes.
• Marks by main topic: Vectors (Mechanics context) 19, Kinematics 19, Moments 12, Dynamics of a Particle 11, Momentum and Impulse 7, Statics of a Particle 7.
• More Moments in other sittings: October 2023 Q1 (5 marks), January 2023 Q4 (8 marks), January 2024 Q5 (10 marks).
• Against the other 15 sittings we mapped: more marks on Moments (12 marks here, 8 on average); fewer on Forces and Newton's Laws (0 marks here, 4 on average).
• Not on this paper: Forces and Newton's Laws.
• Calculator: allowed.

WME01/01: question by question

Labels and topics are ours, read from the WME01/01 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Two particles colliding (7 marks) · M1 Momentum and Impulse
2. Q2Velocity and position with vectors (10 marks) · M1 Vectors (Mechanics context)
3. Q3Book falling from a shelf (8 marks) · M1 Kinematics
4. Q4Beam suspended by two ropes (12 marks) · M1 Moments
5. Q5Speed-time graph of a journey (11 marks) · M1 Kinematics
6. Q6Particle on a rough surface pulled at an angle (7 marks) · M1 Statics of a Particle, M1 Forces and Newton's Laws
7. Q7Car towing a trailer up a slope (11 marks) · M1 Dynamics of a Particle
8. Q8Motion across a square floor with vectors (9 marks) · M1 Vectors (Mechanics context)

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