Moderate -0.8 This is a straightforward one-step momentum conservation problem with all values given and a single unknown. Students simply apply conservation of momentum with particles moving in opposite directions, requiring only substitution into the standard formula m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ with v₂ = 0. This is easier than average as it's a textbook exercise with no problem-solving or conceptual challenges beyond basic recall.
1 Two particles \(P\) and \(Q\) of masses 0.2 kg and 0.3 kg respectively are free to move in a horizontal straight line on a smooth horizontal plane. \(P\) is projected towards \(Q\) with speed \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). At the same instant \(Q\) is projected towards \(P\) with speed \(1 \mathrm {~ms} ^ { - 1 } . Q\) comes to rest in the resulting collision.
Find the speed of \(P\) after the collision.
For conservation of momentum. Dimensions correct. Allow if 3 relevant momentum terms are seen regardless of sign.
Speed \(= 1 \text{ ms}^{-1}\)
A1
Allow if final answer given as \(v = 1\) or speed \(= 1\) from an equation whose solution is \(v = -1\)
[3]
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\pm 0.2 \times 0.5$ or $\pm 0.3 \times 1$ | **B1** | For initial momentum for either particle. Allow kg or g. |
| $0.2 \times 0.5 + 0.3 \times (-1) = 0.2 \times v + 0$ | **M1** | For conservation of momentum. Dimensions correct. Allow if 3 relevant momentum terms are seen regardless of sign. |
| Speed $= 1 \text{ ms}^{-1}$ | **A1** | Allow if final answer given as $v = 1$ or speed $= 1$ from an equation whose solution is $v = -1$ |
| | **[3]** | |
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1 Two particles $P$ and $Q$ of masses 0.2 kg and 0.3 kg respectively are free to move in a horizontal straight line on a smooth horizontal plane. $P$ is projected towards $Q$ with speed $0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. At the same instant $Q$ is projected towards $P$ with speed $1 \mathrm {~ms} ^ { - 1 } . Q$ comes to rest in the resulting collision.
Find the speed of $P$ after the collision.\\
\hfill \mbox{\textit{CAIE M1 2021 Q1 [3]}}