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12.v=u+at is---------------.Equation 1Equation 2Equation 3None of this |
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Answer» To DERIVE : The equations .... v = u + at s = u + 1/2 at² v² = u² + 2as solution : let a PARTICLE moves with INITIAL VELOCITY u after time t, its velocity becomes v due to acceleration acting on particle is a. see figure, slope of velocity - time graph = acceleration ⇒(v - u)/(t - 0) = a ⇒v - u = at ⇒v = u + at .........(1) area enclosed the velocity - time graph = displacement covered by particle ⇒area of TRAPEZIUM formed as shown in figure = S ⇒S = 1/2 [v + u ] × t from equation (1), ⇒S = 1/2 [u + at + u ] × t ⇒S = 1/2 [2u + at] × t ⇒S = ut + 1/2 at² ...........(2) we know, acceleration, a = v dv/ds ⇒a ∫ds = ∫v dv ⇒a[s] = [v²/2] ⇒as = 1/2 [v² - u²] ⇒2as = v² - u² ⇒v² = u² + 2aS ............(3)
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