How Does Displacement Affect Final Velocity in Constant Acceleration?

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SUMMARY

The discussion focuses on calculating the final velocity of a car under constant acceleration when the displacement increases from x to 9x. Using the equation v² = vo² + 2a(x - xo), where the initial velocity (vo) is zero, the final velocity (v) can be derived for the initial displacement. By substituting the new displacement of 9x into the equation, participants clarify how to determine the new final velocity in terms of the original final velocity.

PREREQUISITES
  • Understanding of kinematic equations, specifically v² = vo² + 2a(x - xo)
  • Basic knowledge of constant acceleration concepts
  • Familiarity with displacement and velocity definitions
  • Ability to manipulate algebraic equations
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  • Study the derivation of kinematic equations for constant acceleration
  • Learn how to apply the concept of displacement in physics problems
  • Explore examples of final velocity calculations in various scenarios
  • Investigate the implications of changing displacement on velocity in real-world applications
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Students studying physics, particularly those focusing on kinematics, as well as educators seeking to explain concepts of displacement and velocity under constant acceleration.

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Homework Statement



A car starts from rest, accelerates at a constant rate, has a displacement of x and a final velocity of v. What is the final velocity (in terms of v) if the displacement was 9x?

Homework Equations


v^2=vo^2 + 2a(x-xo)


The Attempt at a Solution


I have no idea. :(
 
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Hello KJD, welcome to PF! You must have some idea! :smile:.
Seems like a 2-part problem. First find v, given:
A car starts from rest, accelerates at a constant rate, has a displacement of x and a final velocity of v.

What would v be in this case, using the equation you provided?

What is the final velocity in terms of v if the displacement was 9x?

Now, jack up x by 9, using your result from the first part. Does this help?
 
Thank you so much! I think I understand now! I just didn't know where to start. Thanks again :smile:
 

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