3: The law of conservation of linear momentum states that in an isolated system, the total linear momentum remains constant. This means that the total momentum before a collision or interaction is e

Let the initial direction of the car be positive.
Mass of car ($m_c$) = $1000 \text{ kg}$
Initial velocity of car ($v_{ci}$) = $+40 \text{ m/s}$
Mass of truck ($m_t$) = $5000 \text{ kg}$
Initial velocity of truck ($v_{ti}$) = $-20 \text{ m/s}$ (since it's moving head-on, in the opposite direction)
After the collision, the car and truck move together with a common final velocity ($v_f$).

The total momentum before the collision equals the total momentum after the collision:

The negative sign indicates that the final velocity is in the opposite direction to the car's initial motion (i.e., in the direction the truck was initially moving).

The velocity of the thief's car immediately after the collision is $\boxed{\text{10 m/s in the direction of the truck's initial motion}}$.

4.5:

Impulse ($J$) is the change in momentum ($\Delta p$). We will calculate the impulse on the car.
$J_c = \Delta p_c = m_c v_f - m_c v_{ci}$
Using the values from 4.4:
$m_c = 1000 \text{ kg}$
$v_{ci} = +40 \text{ m/s}$
$v_f = -10 \text{ m/s}$

The average force ($F_{avg}$) is equal to the impulse divided by the time interval ($\Delta t$).
The collision lasts $\Delta t = 0.5 \text{ s}$.

The magnitude of the average force is $100000 \text{ N}$.

The research states that forces greater than $85000 \text{ N}$ may cause fatal injuries.
Our calculated average force magnitude is $100000 \text{ N}$.
Since $100000 \text{ N} > 85000 \text{ N}$, the collision could result in a fatal injury.

The collision could result in a fatal injury because the calculated average force of $\boxed{\text{100000 N}}$ is greater than the threshold of $85000 \text{ N}$.