How Far Does a Boulder Travel Rolling Downhill with Constant Acceleration?

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SUMMARY

A boulder rolls down a hill with a constant acceleration of 3.69 m/s² for a duration of 7.72 seconds, resulting in a calculated distance of 91.64 meters. The correct formula used is d = v0 * t + 0.5 * a * t², where initial velocity (v0) is zero. Misinterpretations regarding the acceleration value and time duration were clarified, emphasizing the importance of using the given parameters directly from the problem statement.

PREREQUISITES
  • Understanding of kinematic equations, specifically d = v0 * t + 0.5 * a * t²
  • Knowledge of constant acceleration concepts in physics
  • Familiarity with units of measurement for acceleration (m/s²) and time (seconds)
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Study the derivation and applications of kinematic equations in physics
  • Explore real-world examples of constant acceleration scenarios
  • Learn about the effects of friction and incline on rolling objects
  • Investigate advanced topics in dynamics, such as energy conservation in rolling motion
USEFUL FOR

Students studying physics, educators teaching kinematics, and anyone interested in understanding motion under constant acceleration.

Doraneli
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1. A boulder initially at rest rolls down a hill with an acceleration of 3.69m/s^2. If it accelerates for 7.72 seconds, how far will it move?


2. d=v0(initial velocity)t+.5at^2



3. d=(0)(7.72)+.5(-9.8)(3.27)^2
-39.24+-52.4
-91.64m

 
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Doraneli said:
1. A boulder initially at rest rolls down a hill with an acceleration of 3.69m/s^2. If it accelerates for 7.72 seconds, how far will it move?


2. d=v0(initial velocity)t+.5at^2



3. d=(0)(7.72)+.5(-9.8)(3.27)^2

Why is t= 7.72 in the first term and 3.27 in the second?

-39.24+-52.4
Where did the "-39.24" come from? And why the "+-" for the second term?

-91.64m
 
You are using the correct equation, but your values for 'a' and 't' are wrong.
The acceleration of the ball is given to you in the question, so you don't need to use 9.81m/s². And also the time stated in the question is 7.72s.
 

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