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## Homework Statement

This is a question from the June 2009 Regents. The question asks what is the average acceleration of a roller coaster cart as it reaches the bottom of a hill. You know that

V

_{i}= 0 m/s (The cart starts from rest from the top of a hill)

V

_{f}= 46.5 m/s (velocity at bottom of hill)

d = 110 m (This is the height of the hill)

t = 5.3 s (Time it takes for it to start from rest and reach the bottom of the hill)

## Homework Equations

The Kinematics equations on the reference table:

a = Δv / t

d = (V

_{i})t + 1/2at

^{2}

V

_{f}

^{2}= V

_{i}

^{2}+ 2ad

Where V

_{i}is initial velocity, and V

_{f}is final velocity.

## The Attempt at a Solution

According to the answer key:

a = Δv / t

a = (46.5m/s) / 5.3 s

and a = 8.8 m/s

^{2}

However, I did V

_{f}

^{2}= V

_{i}

^{2}+ 2ad

I plugged in all the correct numbers and got 9.8m/s

^{2}

Why isn't my answer valid/ Why do the two formulas yield different answers?

Thank you.