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Use integeration technique to prove that...

Use integeration technique to prove that the distance travelled in nth second: `s_nth=u+frac(a)(2)(2n-1)`

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Questions|Reaction Time |Distance Travelled In nth Second

For a particle moving with constant acceleration, prove that the displacement in the n^(th) second is given by s_(n^(th)) = u + (a)/(2)(2n-1)

Knowledge Check

  • Distance travelled in nth second has the units of

    A
    displacement
    B
    velocity
    C
    acceleration
    D
    momentum

  • Whether a given relation / formula is correct or not can be checked on the basis of the principle of homogeneity of dimensions. According to this principle, only that formula is correct, in which the dimensions of the various terms on one side of the relation are equal to the respective dimensions of these terms on the other side of the relation. With the help of the compreshension given above, choose the most appropriate alternative for each of the following questions : The distance travelledl by a body in nth second is given by S_(nth) = u + (a)/(2) (2n-1) where u is initial velocity and a is acceleration. The dimensions of S_(nth) are

    A
    L
    B
    `LT^(-1)`
    C
    `LT^(-2)`
    D
    `L^(-1)T`

  • With usual notation, the following equation, said to give the distance covered in the n"th" second. i.e., S_(n)=u+a((2n-1))/2 is

    A
    only numerically correct
    B
    only dimensionally correct
    C
    Both dimensionally and numerically
    D
    Neither numerically nor dimensionally correct

    • Similar Questions

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    Questions|Distance Travelled In nth Second |Reaction Time

    Find the initial velocity and acceleration of a body if the distance traveled by that body in nth second is (5.69+0.008n) m

    Find the initial velocity and acceleration of a body if the distance traveled by that body in nth second is (5.96 + 0.08n) m.

    Chek the correctness of the relation, S_(n_(th)) = u +(a)/(2)(2n -1), where u is initial velocity, a is acceleratin and S_(n_(th)) is the distance travelled by the body in nth second.

    Assertion : Distance travelled by the particle in the nth second has dimensios of length. Reason :It is the distance travelled by the partical in the given time.

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