Question

drive this formula s=ut+1/2at squre

Answer 1

Derivation for 2nd equation:- S=ut+1|2at^2.
Condiser a body having initial velocity 'u' and suppose it is subjected to a uniform acceleration on 'a' . So that after time 't' its final velocity becomes 'v' . then the distance travelled (s) by the body in time 't' is given by:

Distance = avg. velocity ×time
= (avg. velocity = u+v|2)

S = (u+v|2)×t
put v= u + at (from equation A)

S= (u+v+at|2) × t
S= (2u+at)×t
S= 2ut+at^2/2
s= 2yt/2 + at^2/2
s = ut + 2at^2.
Finish thank you

Answer 2

s=distance.
here,v=average velocity
t=time
average velocity=v+u/2
velocity=displacement/time=s/t
v×t=s
put the value of v=average velocity
v+u/2×t=s(v=final velocity,u=initial velocity)
put the value of v from 1st equation(v=u+at)
(u+at)+u×t/2=s
(2u+at)×t/2=s
2ut+at^2/2=s
2ut+at^2/2×2=s(2ut÷2=ut and we can write at^2/2as:-1/2at^2)
ut+1/2at^2=s
s=ut+1/2at^2