Question

S= ut + 1/2 at^2



Prove

Answer 1

Acceleration a

d^2s/dt^2=a

Integrate

ds/dt=at +c.. velocity at time t=0 is u

ds/dt=at + u

Integrate

s= (1/2) at^2 + ut + b if distance s = 0 at time t=0 then

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

Answer 2

Displacement or Distance= average velocity time. we know that average velocity= v+u÷2,so ,s= v+u÷2×t on putting v = u+at, s=u+at+u÷2×t=2ut + at^2÷2 ,s = ut + 1/2at^2