s=v0*t+1/2*a*t*t
vt=v0+a*t
so,a*t=vt-v0
so,
s=v0*t+1/2*(vt-v0)*t
=[v0+1/2*(vt-v0)]*t
=(v0+1/2*vt-1/2*v0)*t
=(1/2*v0+1/2*vt)*t
=1/2(v0+vt)*t
=(v0+vt)*t/2