Question #6f221

1 Answer
Feb 7, 2018

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