Uniform Acceleration Motion: Equations with Explanations

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    The equations that quantitatively describes uniform acceleration motion are explained.

    Let
    a be the acceleration
    u be the initial velocity at time t1
    v be the final velocity at time t2
    t = t 2 - t1
    x is the displacement between t1 and t2
    x0 is the initial position

    The relationship between all the above quantities are given by the following equations:

    definition of acceleration: a = (v - u) / t

    v = a t + u 1 (deduced from above definition)
    x = (1/2) a t 2 + u t + x0 2
    x = (1/2)(u + v) t + x0 3
    v 2 = u 2 + 2 a (x - x0) 4

    If x     0 = 0 (start from origin) , the above equations simplifies to
    v = a t + u 1
    x = (1/2) a t 2 + u t 2
    x = (1/2)(u + v) t 3
    v 2 = u 2 + 2 a x 4

    If x     0 = 0 (start from origin) and u =0 (starting from rest) the above equations simplifies further to
    v = at 1
    x = (1/2) a t 2 2
    x = (1/2) v t 3
    v2 = 2 a x 4

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