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The velocity of a particle is v = v0 + gt + ft². If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

1. v0 + g/2 + f/3
2. v0 + 2g + 3f
3. v0 + g/2 + f/3
4. v0 + g + f

Correct answer: v0 + g/2 + f/3

Solution

The correct option is derived from integrating the velocity function to find the displacement. By evaluating the integral of the velocity equation from time 0 to 1, we find that the displacement is v0 + g/2 + f/3, which accounts for the contributions of both the linear and quadratic terms in time.

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