Why isn't acceleration halved in free fall from 50m?

[NafeesR]

Homework Statement

A child accidentally drops her doll from a bridge suspended 50m above a fast moving river. Assuming the doll never reaches terminal velocity, how many seconds will it take for the doll to hit the water?

Homework Equations

x=x₀+ v₀t + 0.5*at²

The Attempt at a Solution

Using acceleration formula: x=x₀+ v₀t + 0.5*at²
It should be 0=(50M)+(0m/s)t+0.5*(-9.8m/s²)
Which would give me 3.194382825 seconds. The textbook's answer is 2.3s. So after a bit of exploration I realized that the acceleration isn't supposed to be halved. That brings me to the question why isn't the acceleration halved like the example and other questions using the formula?

 

[fluidistic]

Homework Statement

A child accidentally drops her doll from a bridge suspended 50m above a fast moving river. Assuming the doll never reaches terminal velocity, how many seconds will it take for the doll to hit the water?

Homework Equations

x=x₀+ v₀t + 0.5*at²

The Attempt at a Solution

Using acceleration formula: x=x₀+ v₀t + 0.5*at²
It should be 0=(50M)+(0m/s)t+0.5*(-9.8m/s²)
Which would give me 3.194382825 seconds. The textbook's answer is 2.3s. So after a bit of exploration I realized that the acceleration isn't supposed to be halved. That brings me to the question why isn't the acceleration halved like the example and other questions using the formula?

Your answer is right (though you made a typo error and forgot a "t" in your equation.)
The factor 1/2 in front of the acceleration comes from integration.