# 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...

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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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 `