Kinematics - Finding position and acceleration

AI Thread Summary
The discussion revolves around solving kinematic equations for a test car's position and acceleration based on its position function x(t) = 2.17 m + 4.80 m/s²t² - 0.100 m/s⁶t⁶. The user attempts to find the first and second instances when the car has zero velocity by deriving the velocity function v(t) and subsequently the acceleration function a(t). They successfully calculated parts a, b, and c but encountered difficulties with their calculations, particularly when determining the correct time values for zero velocity. The user questions whether they should solve for t at v(t) = 0, confirming that this is indeed the correct approach for parts a and c. Overall, the thread highlights challenges in applying derivatives to kinematic equations in a homework context.
MozAngeles
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Homework Statement



The position of the front bumper of a test car under microprocessor control is given by x(t) = 2.17 m + 4.80 m/s2t2 - 0.100 m/s6t6.
a. Find its position at the first instant when the car has zero velocity.
b. Find its acceleration at the first instant when the car has zero velocity.
c. Find its position at the second instant when the car has zero velocity.
d. Find its acceleration at the second instant when the car has zero velocity.

Homework Equations


i took the derivative and to get v(t) for parts a,b,c of this
then the second derivative to get a(t)


The Attempt at a Solution


a(t)= 9.6-3t4 solve for t we get 1.337 when i plug that into the v(t) equation i get ~10 but when i plugg this in it's wrong. I have to idea what is going wrong, this is how my professor set it up... i got a,b,c right though...
 
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Are you not suppose to solve for t at v(t) = 0?
 


yes for part a and c
 

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