Show that the impulse reduces the speed of the particle but does not reverse its direction.

Here are the solutions to the problems:

Question 2:

*a) Show that the impulse reduces the speed of the particle but does not reverse its direction.
Let the initial velocity be $v_i = 4u$. The mass of the particle is $m_p = 2m$.
The impulse $I = 3mu$ is directed opposite to the initial motion. If we take the initial direction as positive, the impulse is $-3mu$.
Using the impulse-momentum theorem: $I = \Delta p = m_p v_f - m_p v_i$.

$$-3mu = (2m)v_f - (2m)(4u)$$ $$$$