Edexcel IAL M1 June 2022 question paper and mark scheme (WME01/01)

Try 3 M1 questions like these

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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 answer

   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 \(\big((1+2t)\mathbf{i}+(5-t)\mathbf{j}\big)\) 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 \(PL^2=5t^2-24t+53\). [2]

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

   Worked answer

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

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

   (b) \(PL^2=(7-2t)^2+(2+t)^2\) 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 answer

   1. M1 for finding the velocity just before impact using $v^2 = u^2 + 2as$: $v_1^2 = 0 + 2(9.8)(19.6) = 19.6^2 \implies v_1 = 19.6 \text{ m s}^{-1}$ downwards.
   2. M1 for finding the velocity just after impact using $v^2 = u^2 + 2as$: $0 = v_2^2 - 2(9.8)(4.9) \implies v_2^2 = 9.8^2 \implies v_2 = 9.8 \text{ m s}^{-1}$ 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

M1 topics this paper can test

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• Kinematics
• Forces and Newton's Laws
• Moments
• Vectors (Mechanics context)
• Dynamics of a Particle
• Statics of a Particle
• Momentum and Impulse

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Formula booklet

Mathematical Formulae and Statistical Tables (International AS/A Level Mathematics) · Pearson Edexcel · For the 2018 IAL specification (current)