Question

Please answer the question

Answer 1

Proof:

average velocity = $\frac{ distance}{time}$

⇒ average velocity =  $\frac{s}{t}$ ...........(1)

and

⇒ average velocity =  $\frac{u+v}{t}$..................(2)

From Equation (1) and (2)

⇒   $\frac{s}{t} = \frac{u+v}{2}$ ...................(3)

The first equation of motion : v = u + at

Substituting the value of v in equation (3)

⇒$\frac{s}{t} = \frac{u+u+at}{2}$

⇒$\frac{s}{t} = \frac{2u+at}{2}$

⇒$s = \frac{( 2u+at)t}{2}$

⇒$s = \frac{2ut+a t^{2} }{2}$

⇒$s = \frac{2ut}{2} + \frac{at^{2} }{2}$       ∵ By canceling 2 in 1st term and taking $\frac{1}{2}$ in 2nd term.

⇒ $s = ut + \frac{1}{2} at^{2}$

Hence Proved .

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