CAIE M1 2021 June — Question 1 4 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2021
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMomentum and Collisions
TypeCollision with two possible outcomes
DifficultyStandard +0.3 This is a standard momentum conservation problem with a straightforward algebraic constraint (v_Q = 2v_P). It requires setting up conservation of momentum, substituting the given relationship, and solving a linear equation. The two solutions arise from considering both possible directions of motion post-collision. This is slightly easier than average as it's a textbook-style mechanics problem with clear setup and routine algebraic manipulation.
Spec6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form
1 Particles \(P\) of mass 0.4 kg and \(Q\) of mass 0.5 kg are free to move on a smooth horizontal plane. \(P\) and \(Q\) are moving directly towards each other with speeds \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively. After \(P\) and \(Q\) collide, the speed of \(Q\) is twice the speed of \(P\). Find the two possible values of the speed of \(P\) after the collision.
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\(0.4 \times 2.5 - 0.5 \times 1.5\)M1 Attempt momentum before impact
\(0.4 \times 2.5 - 0.5 \times 1.5 = 0.4v + 0.5 \times 2v\)M1 Use of conservation of momentum, either case
\(0.4 \times 2.5 - 0.5 \times 1.5 = 0.4v + 0.5 \times 2v\) or \(0.4 \times 2.5 - 0.5 \times 1.5 = -0.4v + 0.5 \times 2v\)A1 One correct equation
Speed is \(0.179\ \text{ms}^{-1}\) or \(0.417\ \text{ms}^{-1}\)A1 Both values 
**Question 1:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| $0.4 \times 2.5 - 0.5 \times 1.5$ | M1 | Attempt momentum before impact |
| $0.4 \times 2.5 - 0.5 \times 1.5 = 0.4v + 0.5 \times 2v$ | M1 | Use of conservation of momentum, either case |
| $0.4 \times 2.5 - 0.5 \times 1.5 = 0.4v + 0.5 \times 2v$ or $0.4 \times 2.5 - 0.5 \times 1.5 = -0.4v + 0.5 \times 2v$ | A1 | One correct equation |
| Speed is $0.179\ \text{ms}^{-1}$ or $0.417\ \text{ms}^{-1}$ | A1 | Both values |

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1 Particles $P$ of mass 0.4 kg and $Q$ of mass 0.5 kg are free to move on a smooth horizontal plane. $P$ and $Q$ are moving directly towards each other with speeds $2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ respectively. After $P$ and $Q$ collide, the speed of $Q$ is twice the speed of $P$.

Find the two possible values of the speed of $P$ after the collision.\\

\hfill \mbox{\textit{CAIE M1 2021 Q1 [4]}}
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