Remember that displacement is the integral of the velocity, so you have o integrate the velocity function between 0 and 6 seconds to find the displacement in the first 6 seconds.
[tex]\int _0^65t-2dt[/tex][tex]d(t)=\frac{5t^2}{2}-2t[/tex][tex]d(6)=\frac{5(6)^2}{2}-2(6)=90-12=78[/tex][tex]d(0)=0[/tex][tex]78-0=78[/tex]So the displacement in the first 6 seconds is 78 meters.
