# Kinematics Question

1. Jun 26, 2009

### AlbanyHS

1. The problem statement, all variables and given/known data
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
Vi = 0 m/s (The cart starts from rest from the top of a hill)
Vf = 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)

2. Relevant equations
The Kinematics equations on the reference table:
a = Δv / t

d = (Vi)t + 1/2at2

Where Vi is initial velocity, and Vf is final velocity.

3. The attempt at a solution

a = Δv / t
a = (46.5m/s) / 5.3 s
and a = 8.8 m/s2

However, I did Vf2 = Vi2 + 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.

2. Jun 26, 2009

### Staff: Mentor

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.

3. Jun 26, 2009

### AlbanyHS

Ah, I see. Thank you for clarifying.