A railway truck P, of mass m kg, is moving along a straight horizontal track with speed 15 ms⁻¹ - Edexcel - A-Level Maths Mechanics - Question 1 - 2012 - Paper 1

To find the value of m, we apply the principle of conservation of linear momentum, which states that the total momentum before the collision equals the total momentum after the collision.

The initial momentum of P is:

$p_{P, initial} = m \times 15 \, \text{ms}^{-1}$

The initial momentum of Q is 0. The total initial momentum is therefore:

$P_{initial} = m \times 15$

After the collision:

• For P: The speed is now -3 ms⁻¹ (since it is moving in the opposite direction).
• For Q: The speed is 9 ms⁻¹.

The total final momentum is:

$P_{final} = m \times (-3) + 3000 \times 9$

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

$m \times 15 = m \times (-3) + 3000 \times 9$

Simplifying:

$m \times 15 + m \times 3 = 27000$ $m \times 18 = 27000$

Dividing both sides by 18 gives:

$m = 1500 \, \text{kg}$