The go-kart's velocity [tex]v[/tex] after time [tex]t[/tex] is given by
[tex]v=v_0+at[/tex]
where [tex]v_0[/tex] is its initial velocity and [tex]a[/tex] is its acceleration. After [tex]t=5\,\mathrm s[/tex], the go-kart stops completely, so
[tex]0\,\dfrac{\mathrm m}{\mathrm s}=v_0+\left(-0.5\,\dfrac{\mathrm m}{\mathrm s^2}\right)(5\,\mathrm s)\implies v_0=2.5\,\dfrac{\mathrm m}{\mathrm s}[/tex]
where [tex]a<0[/tex] because we know the go-kart is slowing down.
