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    If a body starts from rest and moves with uniform acceleration, then
    Question

    If a body starts from rest and moves with uniform acceleration, then

    A.

    v ∝ t

    B.

    s ∝ t

    C.

    v ∝ s

    D.

    s ∝ √t

    Correct option is A

    The correct answer is:(a) v∝t

    When a body starts from rest and moves with uniform acceleration, the following equations of motion apply:

    1. v=u+at, where v is the velocity, u is the initial velocity (0 in this case), a is acceleration, and t is time.

      • Since u=0, v=at, indicating that v∝t

    2. Uniform acceleration implies a constant rate of velocity change.

    3. The relationship s∝t2 can be understood from the second equation of motion: 

    s = ut+12at2

    1. For v2∝s, this comes from the third equation of motion: v2=u2+2as

    Additional Information:

    • s∝t: Incorrect, because the displacement sss is proportional to the square of time under uniform acceleration. From the equation s=ut+12at2, s∝t2 when u=0.

    • v∝s: Incorrect, because v2=u2+2as indicates that v2∝s (not v∝s).

    s∝t​: Incorrect, as s∝t2 under uniform acceleration, not t.

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