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12 December, 17:07

Calculating Final Velocity

A roller coaster is traveling at 13 m/s when it approaches a hill that is 400 m long. Heading down the hill, it accelerates at 4.0 m/s2. What is the final velocity of the roller coaster? Round your answer to the nearest whole number.

m/s

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  1. 12 December, 20:51
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    In physical science, there is an equation that relates the distance, initial velocity, final velocity and acceleration. This equation is written below.

    d = (Vf² - Vi²) / 2a

    where d is the distance,

    Vf is the final velocity,

    Vi is the initial velocity, and

    a is the acceleration

    To get the value of Vf we may rearrange the equation such that,

    Vf² - Vi² = 2ad

    Transposing Vi² to the other side of the equation,

    Vf² = 2ad + Vi²

    Then, we get the square root of each side,

    Vf = sqrt (2ad + Vi²)

    Substitute the given values above,

    Vf = sqrt ((2) (4 m/s²) (400 m) + (13 m/s) ²)

    Vf = 58.04 m/s

    Hence, the final velocity of the roller coaster is approximately 58.04 m/s.
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