Question

s=ut+1/2at^2 prove it

Answer 1

Hey mate....
Here is your answer

If the initial velocity is u...
Final velocity as v...
Time duration as t...
And uniform acceleration as a


Average velocity=(u+v)/2.....1


But by definition, average velocity=total distance travelled/ total time taken. i.e.s/ut......2


From comparing 1 and 2 we get,

(u+v)/2=s/t
s=1/2(u+v)t......3

also we have....v=u+at
So, by substituting the value of v in 3 we get...

s=ut+1/2at^2

Answer 2

$\textbf{ Hello Mate! }$

As we know that area under V-T graph is displacement and area in figure is formed by triangle and rectangle

Area under graph = Area of rectangle + Area of triangle

s = ( l × b ) + ( 1 / 2 × b × h )

s = ( t × u ) + [ 1 / 2 × t × ( v - u ) ]

s = ut + 1 / 2 × t × at [ :. v - u = at ]

$\textbf{ s = ut + 1/2at^2 }$

Have great future ahead!

$\textbf{ Happy Independence Day }$

जय हिन्द!