The velocity of a particle is v = v_0 + gt + ft^2 . If its position is x = 0 at t = 0 , then its displacement after unit time ( t = 1 ) is: - Physics MCQ AIEEE 2007 2026 | ExamTest.live

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The velocity of a particle is v = v_{0} + g t + f t^{2} . If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is:

Solution & Step-by-step Explanation

Displacement x is the integral of velocity with respect to time: x = \int v d t = \int (v_{0} + g t + f t^{2}) d t x = v_{0} t + \frac{1}{2} g t^{2} + \frac{1}{3} f t^{3} + C At t = 0, x = 0 ⟹ C = 0 .For unit time (t = 1): x = v_{0} (1) + \frac{1}{2} g (1)^{2} + \frac{1}{3} f (1)^{3} x = v_{0} + \frac{g}{2} + \frac{f}{3}

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The velocity of a particle is v = v_{0} + g t + f t^{2} . If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is:

v_{0} + 2 g + 3 f

v_{0} + g /2 + f /3

v_{0} + g + f

v_{0} + g /2 + f

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