An inflationary universe scenario in the context of a tachyon field is studied. This study is carried out using an ansatz for the effective potential of cosmological perturbations U(η). We describe in great detail the analytical solutions of the scalar and tensor perturbations for two different Ansätze for the effective potential of cosmological perturbations: Easther's model and an effective potential similar to power-law inflation. Also, we find from the background equations that the effective tachyonic potentials V(φ) in both models satisfy the properties of a tachyonic potential. We consider the recent data from the Planck to constrain the parameters in our effective potential generating the cosmological perturbations.