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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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