1 Two particles, \(A\) and \(B\), are travelling in the same direction with constant speeds along a straight line when they collide. Particle \(A\) has mass 2.5 kg and speed \(12 \mathrm {~ms} ^ { - 1 }\). Particle \(B\) has mass 1.5 kg and speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). After the collision, the two particles move together at the same speed. Find the speed of the particles after the collision.

## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $2.5 \times 12 + 1.5 \times 4 = 4v$ | M1 | Three term momentum equation, correct values but condone incorrect signs |
| Correct equation with correct signs | A1 | |
| $v = \frac{36}{4} = 9 \text{ ms}^{-1}$ | A1 | Correct speed. Consistent use of $mg$ instead of $m$ throughout, deduct 1 mark |
| **Total: 3 marks** | | |

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1 Two particles, $A$ and $B$, are travelling in the same direction with constant speeds along a straight line when they collide. Particle $A$ has mass 2.5 kg and speed $12 \mathrm {~ms} ^ { - 1 }$. Particle $B$ has mass 1.5 kg and speed $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. After the collision, the two particles move together at the same speed.

Find the speed of the particles after the collision.

\hfill \mbox{\textit{AQA M1 2009 Q1 [3]}}