Question

Derive: S = ut + + at 2. 2​

Answer 1

Answer:

We need to do derivation of 2nd Equation Of Kinematics : \large\sf{s = ut + \dfrac{1}{2}a {t}^{2} }s=ut+

2

1

at

2

Now, Solution :-

We know that,

Average Velocity = \large\sf{ \dfrac{u + v}{2} }

2

u+v

And,

Distance = Average Velocity × Time.

Distance = \large\sf{ \dfrac{u + v}{2} \times t }

2

u+v

×t

And, From the First Equation,

Final Velocity = u + at.

Now, Substitute the values.

\dashrightarrow\sf {s = \dfrac{u + u + at}{2} \times t}⇢s=

2

u+u+at

×t

\dashrightarrow\sf{s = \dfrac{2u + at}{2} \times t}⇢s=

2

2u+at

×t

\dashrightarrow\sf{s = \dfrac{\cancel{2}ut}{\cancel{2}} } + \dfrac{ {at}^{2} }{2}⇢s=

2

2

ut

+

2

at

2

\boxed{\dashrightarrow\bf\red{s = ut + \dfrac{ {at}^{2} }{2} }}

⇢s=ut+

2

at

2

Hence, Derived.

I hope its help you

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