A 2578-kg van runs into the back of a 825-kg compact car at rest. They move off together at 8.5 m/s. Assuming the friction with the road is negligible, calculate the initial speed of the van.

The initial speed of the car = 11.22 m/s

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