Two particles P and Q have mass 0.4 kg and 0.6 kg respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2008 - Paper 1

Using the principle of conservation of momentum, the total momentum before the collision must equal the total momentum after the collision.

Before the collision, the momentum of P is:

$\text{Momentum}_{P} = 0.4 \times 7.5 = 3 \text{ kg m s}^{-1}$

The momentum of Q can be computed as:

$\text{Momentum}_{Q} = 0.6 \times 5 = 3 \text{ kg m s}^{-1}$

Let the speed of P after the collision be $v$. Then, the total momentum after the collision is:

$\text{Total Momentum}_{after} = 0.4 v + 3$

Setting the initial total momentum equal to the final total momentum gives:

$3 = 0.4 v + 3$

Solving this equation leads to:

$0.4 v = 0$

Thus, we find:

$v = 0$

This confirms that immediately after the collision, particle P is at rest.