Question

Question #6f221

Answer 1

`v(t)=-6t^2+24t`
Backwards when `tin(-oo,0)uu(4,oo)`
Forward when `tin(0,4)`
Still when `t=0 and t=4`

Explanation:

The position of the object is given by

`x(t)=-2t^3+12t^2`

The relationship between velocity and position is

`x'(t)=v(t)`

By the power rule the object's velocity is

`v(t)=x'(t)=-6t^2+24t`

The object movement must follow:

When `v(t)>0` is moving forward
When `v(t)<0` is moving backwards
When `v(t)=0` is still

Solve the equation `v(t)=0`

`t*(-6t+24)=0=>t=0 or t=4`

Check some points to see whether `v(t)>0 or v(t)<0`

`v(-1)=-30` and `v(1)=18` and `v(5)=-30`

The object moving backwards when `(-oo,0) and (4,oo)`
The object moving forward when `(0,4)`
The object still when `t=0 and t=4`