The velocity of a particle is v = v₀ + gt +f t².If its position is x = 0 at t = 0, then its displacement after unit time (t - 1) is

Given that $\mathrm{v}={\mathrm{v}}_0+\mathrm{gt}+{\mathrm{ft}}^2$
or $\frac{\mathrm{dx}}{\mathrm{dt}}={\mathrm{v}}_0+\mathrm{gt}+{\mathrm{ft}}^2$
Integrating this expression, we get 
$\mathrm{x}={\mathrm{v}}_0\mathrm{t}+\frac{1}{2}{\mathrm{gt}}^2+\frac{1}{3}{\mathrm{ft}}^2+\mathrm{C}$
where C is integration constant.
When x=0 and t = 0, C = 0
$∴\mathrm{x}={\mathrm{v}}_0\mathrm{t}+\frac{1}{2}{\mathrm{gt}}^2+\frac{1}{3}{\mathrm{ft}}^2$
The required displacement
$={\mathrm{v}}_0+\frac{1}{2}\mathrm{g}+\frac{1}{3}\mathrm{f}$