Two particles P and Q have masses 4m and m respectively - Edexcel - A-Level Maths Mechanics - Question 1 - 2013 - Paper 1

To find the speed and direction of motion of Q after the collision, we can apply the principle of conservation of momentum.

The total momentum before the collision can be expressed as:

$p_{initial} = (4m)(2u) + (m)(-5u) = 8mu - 5mu = 3mu$

Let ( v ) be the speed of Q after the collision. Since the direction of motion is reversed for P, we incorporate that:

The total momentum after the collision will be:

$p_{final} = m(v) - 4m\left(\frac{1}{2}u\right) = mv - 2mu$

Setting the initial momentum equal to the final momentum gives:

$3mu = mv - 2mu$

Rearranging this equation yields:

$3mu + 2mu = mv \Rightarrow 5mu = mv \Rightarrow v = 5u$

Thus, the speed of Q after the collision is ( 5u ) and it is moving in the same direction as before the collision.