Question

s=ut+1/2at^ DERIVE PLEASE ❤❤​

Answer 1

Hlew,

Here's your answer...

We can derive this equation by two methods - by Graphical and by Calculus.

So, Firstly we derive by Graphical Method :-

See the graph below,

Distance travelled = Area of rectangle ( OADC ) + Area of triangle ( ΔABD)

s = ( OA * AD ) + 1/2 * AD * BD

s = ( u * t ) + 1/2 * t * at

s = ut + 1/2 at²

_______________________________________________________

By Calculus method,

v = ds/dt

ds= vdt

ds = ( u + at ) dt

ds = udt + atdt

Integrating both sides,

∫ ds = u ∫ dt + a ∫ dt²

[ s ]ᵃ₀ = u [ t ]₀ + a [ t²/2 ] ₀

( s - 0 ) = u ( t - 0 ) + a ( t²/2 - 0 )

s = ut + 1/2 at²

Thanks.

Sorry baby 'wink'

Answer 2

Answer:S=UT+1/2AT^2

Explanation:

V(average) = (U+V)/2

S/T = (U+V)/2

2S = (U+V)T

2S = [U+(U+AT)]T

since,V=U+AT

2S = (2U+AT)T

2S = 2UT+AT^2

S = (2UT)/2 + (AT^2)/2

Therefore,

S=UT+1/2AT^2☺

Hope it helps......