Vector dynamics question starting from accelaration

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SUMMARY

The discussion focuses on solving a physics problem involving the acceleration of a particle defined as a = -8 m/s². The participant attempts to integrate the acceleration to find velocity and displacement but encounters difficulties with the initial conditions provided. Key insights include the necessity of incorporating constants of integration and the importance of correctly applying initial conditions to derive accurate results. The conversation emphasizes the mathematical principles of integration in kinematics.

PREREQUISITES
  • Understanding of basic kinematics concepts, including acceleration, velocity, and displacement.
  • Proficiency in calculus, specifically integration techniques.
  • Familiarity with initial conditions in differential equations.
  • Knowledge of particle motion equations in physics.
NEXT STEPS
  • Study the integration of acceleration to derive velocity and displacement in kinematics.
  • Learn how to apply initial conditions in solving differential equations.
  • Explore the concept of constants of integration and their significance in physics problems.
  • Review examples of particle motion problems involving constant acceleration.
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Students in physics, particularly those studying kinematics, as well as educators and tutors looking to enhance their understanding of integration in motion equations.

vladilinsky
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Homework Statement


I took this right out of the text, it is not home work just me trying to get better.

The acceleration of a particle is defined by the relation a = -8 m/s^2
Knowing that x = 20 m when t= 4 m, and that x = 4 m when v = 16 m/s
(a) determine the time when velocity is zero and (b) the velocity and total distance traveled when t = 11 s

Homework Equations


The Attempt at a Solution


My attempt is I know velocity must be the integration of acceleration and displacement the integration of velocity. So I attempted to integrate -8dt 2 times. but when I do that I get x=-4t^2 which does not fit my given when t=4, x=20
Any help would be greatly appreciated, even just pointing me in the right direction
 
Physics news on Phys.org
Looks like you need to take initial conditions into account. Remember that when you integrate you have a constant of integration as well, which you can determine if you have initial conditions (which you have).
 
How do I know which of the conditions to use for the initial conditions?
 

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