**derive the second equation of motion**

Q1- Deduce the expression for the distance travelled by a body moving with uniform acceleration, in a given time.

Or

Deduce the relation :** s = ut + at²/2**, where the symbols used have their usual meanings.

Ans. **Second equation of motion**. Suppose the body starts with initial velocity u and due to uniform acceleration a, its final velocity becomes v after time t. Then

Average velocity =**(Initial velocity + Final velocity)/2**

** = (u +v) / 2**

So, the distance covered by the body in time t is

S = Average velocity x Time

=[u+(v x t)]/2

=[u + (u + at) x t] / 2 [v=u+at]

= (2u + at^{2})/2** S= ut + at ^{2}/2**

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