Calculate Average Acceleration for Kinematics Question

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SUMMARY

The discussion centers on calculating average acceleration for a roller coaster cart using kinematics equations. The correct average acceleration is determined using the formula a = Δv / t, yielding a result of 8.8 m/s², while an alternative method using Vf² = Vi² + 2ad incorrectly gives 9.8 m/s² due to the use of height instead of the distance traveled along the hill. The distinction between vertical height and distance along the slope is crucial for accurate calculations. Participants clarify that velocity and acceleration must be considered parallel to the hill's surface.

PREREQUISITES
  • Understanding of kinematics equations, specifically a = Δv / t and Vf² = Vi² + 2ad.
  • Knowledge of initial and final velocity concepts in physics.
  • Familiarity with the distinction between vertical height and distance traveled along a slope.
  • Basic grasp of acceleration and its units (m/s²).
NEXT STEPS
  • Review the derivation and application of kinematics equations in physics problems.
  • Explore the concept of vector components in motion along inclined planes.
  • Study the implications of using different distances in kinematic calculations.
  • Practice solving similar problems involving average acceleration and distance on slopes.
USEFUL FOR

Students studying physics, educators teaching kinematics, and anyone seeking to improve their problem-solving skills in motion analysis.

AlbanyHS
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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
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)

Homework Equations


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

d = (Vi)t + 1/2at2

Vf2 = Vi2 + 2ad

Where Vi is initial velocity, and Vf 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 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.
 
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AlbanyHS said:
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?
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.
 
Ah, I see. Thank you for clarifying.
 

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