Finding the x range using curvilinear motion

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SUMMARY

The discussion focuses on solving a physics problem involving curvilinear motion of a car moving along a hill defined by the equation y = 16 - (1/625)x². The car's speed is given by V = (25 - 0.15s) m/s, and the task is to determine the car's acceleration at point B, where S = 51.5 m. The user successfully resolved the issue by utilizing the integral of the square root of 1 plus the derivative of y with respect to x to find the x range, allowing for the calculation of the vertical velocity (Vy).

PREREQUISITES
  • Understanding of curvilinear motion and acceleration
  • Familiarity with calculus, specifically derivatives and integrals
  • Knowledge of kinematic equations and their applications
  • Ability to interpret and manipulate mathematical functions
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  • Learn about the integral of the square root of 1 plus the derivative for curve length
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Homework Statement



The car passes point A with a speed of 25 m/s after which its speed is defined by V = (25-0.15s)m/s. Determine the magnitude of the car's acceleration when it reaches point B, where S = 51.5 m. (the max height of the hill is 16 m, and the function of the hill the car is on is y = 16 -(1/625)x^2. A intersects the axis at the furthest point from the origin in the positive direction. S (the Car) is left of A between A and B.)

Homework Equations



The position and velocities given and the radius of curvature (rho) equation.

The Attempt at a Solution


I've solved this problem, that is, the magnitude of an and at. However, an is in terms of x because I can't figure out how to get an x range. I know if I had a "let x = #" I would plug it into the y = 16 -(1/625)x^2 and crunch it to get a Vy, so I'm stuck. Thanks in advance...
 
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Cancel...I solved it...I needed to use intsqrt1+dy/dx to find x, then just plug and chug...
 

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