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26 December, 15:22

The motion of an object undergoing constant acceleration can be modeled by the kinematic equations. One such equation is xf=xi+vit+12at2 where xf is the final position, xi is the initial position, vi is the initial velocity, a is the acceleration, and t is the time. Let's say a car starts with an initial speed of 15 m/s, and moves between the 1000 m and 5000 m marks on a roadway in a time of 60 s. What is its acceleration?

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  1. 26 December, 15:52
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    a = 1.72 m/s²

    Explanation:

    The given kinematic equation is the 2nd equation of motion. The equation is as follows:

    xf = xi + (Vi) (t) + (1/2) (a) t²

    where,

    xf = the final position = 5000 m

    xi = the initial position = 1000 m

    Vi = the initial velocity = 15 m/s

    t = the time taken = 60 s

    a = acceleration = ?

    Therefore,

    5000 m = 1000 m + (15 m/s) (60 s) + (1/2) (a) (60 s) ²

    5000 m = 1000 m + 900 m + a (1800 s²)

    5000 m = 1900 m + a (1800 s²)

    5000 m - 1900 m = a (1800 s²)

    a (1800 s²) = 3100 m

    a = 3100 m/1800 s²

    a = 1.72 m/s²
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