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I am wondering what is the difference between v=s/t & dv = ds/dt where v-velocity,s-displacement,t-time.

Consider Gallelio's equations->

v=u+at--(equation-1) &

s=ut+1/2at^2--(equation-2)

where u-initial velocity & a-acceleration

My doubt is on following point;

If we do,v = s/t in equation-2,we get->v=u+1/2at not v=u+at

but if we do,dv=ds/dt in equation-2,we get=>v=u+at ,exactly the equation we want.

why only differentiation give the result,not just mere divison?????