Kinetmatics of rectilinear motion

AI Thread Summary
A point P accelerates uniformly from rest to 88 ft/sec over 120 ft, leading to an acceleration of 32 ft/s². The discussion highlights 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. It also raises concerns about the relationship between position, velocity, and acceleration in kinematics. Participants suggest using standard kinematics equations for clarity. The overall focus is on understanding the integration process and its implications in rectilinear motion.
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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

  • equation answer.gif
    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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