Velocity of a particle

Question

The velocity function (in meters per second) for a particle moving along a line is given by v(t)=t^3−2t^2. Find the displacement and the distance traveled by the particle during the time interval [-2,4]. 

Displacement = 

Distance traveled =

Answer 1

v(t)=t^3-2t^2= t^2(t-2)=0

t=0, 2

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

s(-2)=28/3 +c

s(4)=64- 128/3+c=64/3+c

displacement =64/3-28/3 = 12 meters

distance traveled =12+2(28/3 +4/3) = 100/3 33 1/3 meters

it moves back and forth from 28/3 to -4/3 and back, changing directions