Velocity and Displacement: How to Derive Expressions from Acceleration Equation

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SUMMARY

The discussion focuses on deriving expressions for velocity and displacement from the given acceleration equation a = 18t - 4. The initial conditions specify that both initial velocity and displacement are zero. By substituting the definition of acceleration as a = dv/dt into the equation, participants can derive the velocity expression v(t) and subsequently the displacement expression x(t) through integration. This method provides a systematic approach to solving kinematics problems in physics.

PREREQUISITES
  • Understanding of basic calculus, specifically integration and differentiation.
  • Familiarity with kinematic equations in physics.
  • Knowledge of initial conditions in motion problems.
  • Concept of acceleration as the rate of change of velocity.
NEXT STEPS
  • Study the process of integrating acceleration to find velocity.
  • Learn how to integrate velocity to derive displacement.
  • Explore the application of initial conditions in solving kinematic equations.
  • Review examples of similar problems involving variable acceleration.
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and motion analysis, as well as educators seeking to enhance their teaching methods in these topics.

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Homework Statement



The acceleration a ms^-2 of a car is given by a=18t - 4 where t is the time in seconds.Derive expressions for the velocity v ms^-1 and the displacement x m if the initial velocity and displacement are both zero

Homework Equations





The Attempt at a Solution


would really appreciate any help with this.I have no idea where to start!Trying to get a sample answer so i can study it to past exam paper questions
 
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Start with the definition of acceleration:

acceleration is the rate of change of velocity, so a= dv/dt.

If you replace 'a' by 'dv/dt' in your equation, can you find 'v'?
 

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