1.

Mathematically prove that the distance (S) travelled by an object is the average mean of initial velocity (u) and final velocity (v) having constant acceleration (a) in the direction of motion in a straight line.

Answer»

SOLUTION :To prove `S = ½ (u+v) t`
We KNOW that `(v = u + "at")`
And 2 as `=v^(2) -u^(2)`
`rArr 2AS =(v-u) (v+u) ( :. a^(2)-b^(2)) = (a +b) (a-b)`
`rArr 2 as = (v + u)` at
`2S = (v + u) t`
or `S = ½ (u + v)t`
`rArr (u + v)//2` is the average velocity


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