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5 November, 17:34

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.

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  1. 5 November, 17:55
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    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
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