1.1 Define the term impulse. 3.1.2 Calculate the magnitude of the force that the truck exerts on the car during the collision, if the collision lasted 0.2 s.

here are the solutions for Questions 3 and 4.

Question 3

3.1.1 Define the term impulse.

Impulse is the product of the net force acting on an object and the time interval over which the force acts. It is also defined as the change in momentum of an object.

3.1.2 Calculate the magnitude of the force that the truck exerts on the car during the collision, if the collision lasted 0.2 s.

Step 1: Identify the given values and set the positive direction.
Let the direction to the right be positive.
Mass of car ($m_c$) = $500 \text{ kg}$
Initial velocity of car ($u_c$) = $7 \text{ m}\cdot\text{s}^{-1}$
Final velocity of car ($v_c$) = $9 \text{ m}\cdot\text{s}^{-1}$
Time of collision ($\Delta t$) = $0.2 \text{ s}$

Step 2: Calculate the change in momentum of the car.

$$\Delta p_c = m_c (v_c - u_c)$$ $$\Delta p_c = 500 \text{ kg} \times (9 \text{ m}\cdot\text{s}^{-1} - 7 \text{ m}\cdot\text{s}^{-1})$$ $$\Delta p_c = 500 \text{ kg} \times (2 \text{ m}\cdot\text{s}^{-1})$$ $$\Delta p_c = 1000 \text{ kg}\cdot\text{m}\cdot\text{s}^{-1}$$

Step 3: Calculate the force exerted on the car using the impulse-momentum theorem ($F = \frac{\Delta p}{\Delta t}$).

$$F = \frac{\Delta p_c}{\Delta t}$$ $$F = \frac{1000 \text{ kg}\cdot\text{m}\cdot\text{s}^{-1}}{0.2 \text{ s}}$$ $$F = 5000 \text{ N}$$

The magnitude of the force is $\boxed{\text{}5000 \text{ N}\text{}}$

3.1.3 Immediately after the collision, the driver of the truck brakes and comes to a stop within 1.5 s. Calculate the magnitude of the acceleration of the truck.

Step 1: Use the principle of conservation of momentum to find the truck's velocity immediately after the collision ($v_t$).
Let the direction to the right be positive.
Mass of truck ($m_t$) = $1200 \text{ kg}$
Initial velocity of truck ($u_t$) = $21 \text{ m}\cdot\text{s}^{-1}$

$$m_c u_c + m_t u_t = m_c v_c + m_t v_t$$ $$$$