Kinetmatics of rectilinear motion

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SUMMARY

The discussion centers on the kinematics of rectilinear motion, specifically calculating the acceleration of a point P that accelerates uniformly to a speed of 88 ft/sec over a distance of 120 ft. The calculated acceleration is 32 ft/s². The user expresses confusion regarding the integration of velocity and acceleration, questioning why velocity is integrated with respect to dv while acceleration is integrated with respect to time. The conversation suggests using standard kinematics equations for clarity.

PREREQUISITES
  • Understanding of basic kinematics equations
  • Familiarity with calculus concepts, particularly integration
  • Knowledge of uniform acceleration principles
  • Ability to interpret motion graphs and equations
NEXT STEPS
  • Study the standard kinematics equations for uniformly accelerated motion
  • Learn about the relationship between velocity, acceleration, and time
  • Explore integration techniques in calculus, focusing on motion equations
  • Review examples of rectilinear motion problems to reinforce concepts
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Students studying physics, particularly those focusing on mechanics and kinematics, as well as educators seeking to clarify concepts of motion and acceleration.

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Homework Statement



A point P starts from rest and accelerates uniformly (meaning x'' = constant) to a speed of 88 ft/sec after traveling 120 ft. Find the acceleration of P.

Homework Equations



x=position
v=velocity=dx/dt
a=acceleration=dv/dt


The Attempt at a Solution



The answer is 32 ft/s^2. Please look at the attachment for the solution. I don't understand it. Why is v integrated with respect to dv while the acceleration x'' is integrated with respect to t? Also wouldn't the integral of v give the position while the integral of acceleration give the velocity? How are they then equal? Sorry but I'm confused about this. Any help appreciated thanks!
 

Attachments

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    equation answer.gif
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The attachment does not appear to be any sort of solution.

Why not use the standard kinematics equations?
 

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