Question

How do we get the formula
Displacement =ut+1/2at^2

Answer 1

acceleration = change in velocity per unit time
                     = (v-u)/t where v-final velocity and u-initial velocity
v-u=at
v=u+at
we know that displacement per unit time is velocity
v= ds/dt
ds/dt = u + at
integrating on both sides then
      since integral of x^n = (x^n+1)/n+1
s= ut + 1/2 at^2 + c
when time is 0 then the body's displacement is also zero
so t=0 , s=0 then c=0
therefore s= ut+1/2 at^2