The velocity of a particle is $$v = (v_0 + gt + Ft^2)$$ m s$$^{-1}$$. Its position is $$x = 0$$ at $$t = 0$$; then its displacement after time ($$t = 1$$ s) is:

We are given the velocity of a particle as $$v = v_0 + gt + Ft^2$$ and the initial position $$x = 0$$ at $$t = 0$$. The displacement is obtained by integrating the velocity with respect to time.

$$x = \int_0^t v \, dt = \int_0^t (v_0 + gt + Ft^2) \, dt = v_0 t + \frac{g t^2}{2} + \frac{F t^3}{3}$$

Substituting $$t = 1$$ s, we get $$x = v_0(1) + \frac{g(1)^2}{2} + \frac{F(1)^3}{3} = v_0 + \frac{g}{2} + \frac{F}{3}$$.