**Answer:**

**<em>The initial speed of the car = 11.22 m/s</em>**

**Explanation:**

**Law of conservation of energy:** It states that when two bodied collide in a closed system, the sum of momentum before collision is equal to the sum of momentum after collision.

<em>**Note:**</em> A close system is one that is free from from external forces. E.g Frictional force.

From the law of conservation of momentum,

Total momentum before collision = Total momentum after collision.

m₁u₁ + m₂u₂ = (m₁ + m₂)V..................... Equation 1

Where m₁ = mass of the van, m₂ = mass of the car, u₁ = initial velocity of the van, u₂ = initial velocity of the car, V = Common velocity.

**<em>Given: m₁ = 2578 kg, m₂ = 825 kg, u₂ = 0 ( the car was at rest), V= 8.5 m/s</em>**

<em>Substituting these values into equation 1, and solving for u₁</em>

<em>2578(u₁) + (825 × 0) = (2578 + 825)8.5</em>

<em>2578u₁ = 28925.5</em>

<em>Dividing both side of the equation by the coefficient of u₁</em>

<em>2578u₁/2578 = 28925.5/2578</em>

<em>u₁ = 11.22 m/s</em>

**<em>The initial speed of the car = 11.22 m/s</em>**