General Question about curved motion

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SUMMARY

The discussion focuses on determining when the speed of an object in curved motion is increasing. The user successfully solved the initial parts of the problem using the dot product and identified when the speed is constant by setting the equation 2t^3 + 6t^2 - 8t equal to zero, yielding critical points at t = -4, t = 1, and t = 0. The user then inquired about the conditions for increasing speed, specifically questioning if a(parallel) * cos(theta) = 0 indicates this. Ultimately, the user confirmed they figured out the solution.

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  • Understanding of curved motion dynamics
  • Familiarity with the dot product in vector mathematics
  • Knowledge of acceleration components (parallel and perpendicular)
  • Basic calculus for solving polynomial equations
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Homework Statement


When if ever is the speed of the object increasing?

Homework Equations


Dot product result, cos(theta) acceleration perpendicular, acceleration parralel

The Attempt at a Solution



I solved the problems first three parts and found when the objects speed is constant using the dot product, now i am trying to figure out how to find if it is increasing. Is it when a(parrelel)*cos(theta) = 0? i have my result from the dot product as 2t^3+6t^2-8t. i set it equal to 0 to find when speed is constant and got t=-4,t=1,t=0. Now i need to find speed increasing and am not sure exactly
 
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I FIGURED IT OUT!!
 

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