IIT JEE , AIEEE Forum - Physics , Mechanics

stavan110

body starts from rest with uniform acceleration .its velocity after 2n seconds is v* .the displacement of da body in last n seconds is????????

the displacement of the body in the t^thsecond of its motion is given by the formula
S = u + at - 1/2a

so the diaplacement of the body in 2n seconds is given as

2na - 1/2a = S

a(2n - 1/2) = S

S/a = 2n - 1/2

S/a + 1/2 = 2n

S/2a + 1/4 = n ...............(1)

similarly the displacement of the body in 'n' seconds will be given as..

S_n = u + an - 1/2a

now the body starts from rest.... so u = 0....

S = an - 1/2a

S = a(S_2n/2a - 1/2a)

S = a(S_2n - 1/2a) (here a big slash stands for " the whole divided by")

S = S_2n - 1/2

So displacement in 'n' seconds is S_n = S_2n - 1/2.......

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