This paper presents spectral and photometric observations of 10 type Ia supernovae (SNe Ia) with redshifts between 0.16 and 0.62. These observations, combined with previous data from the High-Z Supernova Search Team, provide constraints on cosmological parameters such as the Hubble constant (H₀), mass density (Ωₘ), cosmological constant (ΩΛ), deceleration parameter (q₀), and the age of the Universe (t₀). The distances of high-redshift SNe Ia are found to be 10% to 15% farther than expected in a low mass density universe without a cosmological constant. The data strongly favor models with a positive cosmological constant (ΩΛ > 0) and current acceleration of the expansion (q₀ < 0). With no prior constraint on mass density other than Ωₘ ≥ 0, the data are statistically consistent with ΩΛ > 0 at 3.0σ and 4.0σ confidence levels. For a flat universe (Ωₘ + ΩΛ = 1), the data require ΩΛ > 0 at 7σ and 9σ confidence levels. A universe closed by ordinary matter (Ωₘ = 1) is ruled out at 7σ to 8σ confidence levels. The dynamical age of the Universe is estimated to be 14.2 ± 1.5 Gyr, including systematic uncertainties in the Cepheid distance scale. The study also evaluates the effect of systematic errors, including progenitor and metallicity evolution, extinction, sample selection bias, local perturbations in the expansion rate, gravitational lensing, and sample contamination. None of these effects reconcile the data with ΩΛ = 0 and q₀ ≥ 0. The paper also describes the observations, data, and analysis methods used to determine the cosmological parameters. The results indicate that the universe is accelerating and that a positive cosmological constant is required to explain the data. The Hubble constant is estimated to be 65.2 ± 1.3 km s⁻¹ Mpc⁻¹ using the MLCS method and 63.8 ± 1.3 km s⁻¹ Mpc⁻¹ using the template fitting method. The study provides strong evidence for an accelerating universe and a non-zero cosmological constant.This paper presents spectral and photometric observations of 10 type Ia supernovae (SNe Ia) with redshifts between 0.16 and 0.62. These observations, combined with previous data from the High-Z Supernova Search Team, provide constraints on cosmological parameters such as the Hubble constant (H₀), mass density (Ωₘ), cosmological constant (ΩΛ), deceleration parameter (q₀), and the age of the Universe (t₀). The distances of high-redshift SNe Ia are found to be 10% to 15% farther than expected in a low mass density universe without a cosmological constant. The data strongly favor models with a positive cosmological constant (ΩΛ > 0) and current acceleration of the expansion (q₀ < 0). With no prior constraint on mass density other than Ωₘ ≥ 0, the data are statistically consistent with ΩΛ > 0 at 3.0σ and 4.0σ confidence levels. For a flat universe (Ωₘ + ΩΛ = 1), the data require ΩΛ > 0 at 7σ and 9σ confidence levels. A universe closed by ordinary matter (Ωₘ = 1) is ruled out at 7σ to 8σ confidence levels. The dynamical age of the Universe is estimated to be 14.2 ± 1.5 Gyr, including systematic uncertainties in the Cepheid distance scale. The study also evaluates the effect of systematic errors, including progenitor and metallicity evolution, extinction, sample selection bias, local perturbations in the expansion rate, gravitational lensing, and sample contamination. None of these effects reconcile the data with ΩΛ = 0 and q₀ ≥ 0. The paper also describes the observations, data, and analysis methods used to determine the cosmological parameters. The results indicate that the universe is accelerating and that a positive cosmological constant is required to explain the data. The Hubble constant is estimated to be 65.2 ± 1.3 km s⁻¹ Mpc⁻¹ using the MLCS method and 63.8 ± 1.3 km s⁻¹ Mpc⁻¹ using the template fitting method. The study provides strong evidence for an accelerating universe and a non-zero cosmological constant.