Q. 35 A

Derive the formula: $s = ut + \frac{1}{2} at^{2}$,where the symbols have usual meanings.

Let the distance traveled by the body be “s”.

We know that, Distance = Average velocity × Time

Also, Average velocity = $\frac{u+v}{2}$

.: Distance (s) = $\frac{u+v}{2}\times t$ …….eq.(1)

Again we know that: v = u + at substituting this value of “v” in eq.(1), we get

s = $\frac{u+u+at}{2}\times t$

s =$\frac{2u+at}{2}\times t$

s = $\frac{2ut+at^{2}}{2}$

s = $ut+\frac{at^{2}}{2}$

or  $s = ut + \frac{1}{2} at^{2}$

This is the 2nd equation of motion.

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