Answer:
The initial speed of the car = 11.22 m/s
Step-by-step 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.
Note: 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.
Given: m₁ = 2578 kg, m₂ = 825 kg, u₂ = 0 ( the car was at rest), V= 8.5 m/s
Substituting these values into equation 1, and solving for u₁
2578(u₁) + (825 × 0) = (2578 + 825)8.5
2578u₁ = 28925.5
Dividing both side of the equation by the coefficient of u₁
2578u₁/2578 = 28925.5/2578
u₁ = 11.22 m/s
The initial speed of the car = 11.22 m/s