Question

derive the formula s=ut+1/2at^2

Answer 1

We know that,
Average velocity=u+v/2
Distance traveled=average velocity×time
s=u+v/2×t
s=(u+u+at)×t/2. {v=u+at)
s=(2ut+at²)/2
s=2ut/2+at²/2
s=ut+1/2at²
HOPE IT WAS HELPFUL

Answer 2

 we know that average velocity= u+v/2
also, distance travelled = average velocity * time
                   s= (u+v)/2*t ................................1
   from first equation of motion we have,v = u +at put this value in 1
  s = (u+u+at)/2*t
s= (2u+at)/2*t
s=  2ut + at^2/2
s = ut +1/2at^2