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the position of an object at any time is given by the equation s(t)=3t^3-2t+4 find the...

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rmunoz90 | Student, Undergraduate | Salutatorian

Posted April 10, 2013 at 1:53 AM via web

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the position of an object at any time is given by the equation

s(t)=3t^3-2t+4

find the equations of its velocity and its acceleration .(the equation are to be in terms of t)

Its velocity is given by v(t)=

its acceleration is given by a(t)=

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mlehuzzah | Student, Graduate | (Level 1) Associate Educator

Posted April 10, 2013 at 2:03 AM (Answer #1)

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The velocity of the object is the derivative of its position function.
The acceleration of the object is the derivative of its velocity function.

`s(t)=3t^3-2t+4`


The derivative of `a x^n` is `a n x^(n-1)`
The derivative of `c x ` is c
The derivative of a constant is 0

So:

`v(t)=s'(t)=9 t^2 - 2`

`a(t)=v'(t)=18 t `

 

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