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Matter In Our Surroundings

Question
CBSEENSC9005729

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



Solution

Second equation of motion gives us the distance travelled by a body moving with uniform acceleration, in a given time.
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 is given by, 

fraction numerator Initial space velocity space space plus space Final space velocity over denominator 2 end fraction space equals space fraction numerator straight u plus straight v over denominator 2 end fraction

So comma space the space distance space covered space by space the space body space in space time space straight t space is comma space

space straight s space equals space Average space velocity space cross times space Time

space space space space equals fraction numerator straight u plus straight v over denominator 2 end fraction cross times straight t space
space space space space equals space fraction numerator straight u plus left parenthesis straight u plus at right parenthesis over denominator 2 end fraction cross times space straight t space space space space space space space open square brackets because space straight v space equals space straight u space plus space at close square brackets space space space space space space space space space space space space space space space space
space space space space space space space space space equals space fraction numerator 2 ut plus at squared over denominator 2 end fraction
rightwards double arrow space straight s space equals space u t plus 1 half a t squared