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)=

### 1 Answer | Add Yours

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 `

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes