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The Initial velocity of a particle is u (at t = 0) and the acceleration f is given by at. which of the following relation is valid

  1. v = u + at2
  2. v = u + at2/2
  3. v = u at
  4. v = u

Correct answer is (2) Please do with necessary explanation

Kindly do it and check again and don't refer to any other question beacause one such question has been done but its answer is not valid.

Acceleration f is given by:f = atwhere a is constant, t is timef = dvdt  = atdv =at dtintegrate both sides∫uvdv = ∫0tat dtas intial time is 0 and final time is tinitial velocity is u and final velocity is v.we getv - u = 12at2v = u + 12at2

Hence option (2) is correct.

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we have to use integration here,

F= at

dv/dt =at

dv=dtat

then just integrate it. n u will get-

v-u = at^2/2

that is .... v= u+ 1/2 at^2

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