Calculate Average Acceleration for Kinematics Question

[AlbanyHS]

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 + 1/2at²

V_f² = V_i² + 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/s²

However, I did V_f² = V_i² + 2ad

I plugged in all the correct numbers and got 9.8m/s²

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

Thank you.

 

[Doc Al]

However, I did V_f² = V_i² + 2ad

I plugged in all the correct numbers and got 9.8m/s²

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

Realize that the velocity and acceleration are parallel to the hill surface, not straight down. If you use that formula, you need d = distance traveled down the hill, not the height of the hill.

 

[AlbanyHS]

Ah, I see. Thank you for clarifying.