Edexcel IAL M1 October 2020 question paper and mark scheme (WME01/01)

Try 3 M1 questions like these

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1. Kinematics · 5 marks

   Car A travels along a straight road at a constant speed of $25 \text{ m s}^{-1}$. Car B starts from rest at the same point and accelerates uniformly at $3 \text{ m s}^{-2}$ until it reaches a speed of $30 \text{ m s}^{-1}$, after which it maintains this speed. Find the distance Car B travels before it catches up to Car A.

   Worked answer

   1. M1 for finding the time taken for Car B to reach $30 \text{ m s}^{-1}$: $t = \frac{30}{3} = 10 \text{ s}$.
   2. M1 for finding the distances covered in the first $10 \text{ s}$: Car B covers $\frac{1}{2} \times 10 \times 30 = 150 \text{ m}$. Car A covers $25 \times 10 = 250 \text{ m}$.
   3. M1 for setting up an equation for the remaining distance where Car B catches A. Let $t_2$ be the additional time: $150 + 30t_2 = 250 + 25t_2$.
   4. M1 for solving to find $t_2$: $5t_2 = 100 \implies t_2 = 20 \text{ s}$. Total time = $30 \text{ s}$.
   5. A1 for finding the total distance: $25 \times 30 = 750 \text{ m}$.

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

   Two particles A and B, of masses $m$ and $km$ respectively, collide on a smooth horizontal surface. Before the collision, A is moving with speed $3u$ and B is at rest. After the collision, A rebounds with speed $u$ and B moves with speed $u$. Find the value of $k$.

   Worked answer

   1. M1 for applying conservation of momentum, taking A's initial direction as positive.
   2. M1 for the equation: $m(3u) + km(0) = m(-u) + km(u)$.
   3. A1 for simplifying: $3mu = -mu + kmu \implies 4mu = kmu$.
   4. A1 for finding $k = 4$.

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)