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If the velocity of a particle is v = At ...

If the velocity of a particle is `v = At + Bt^2`, where `A` and `B` are constant, then the distance travelled by it between `1 s` and `2 s` is :

A

`(3)/(2) A + 4 B`

B

`3A + 7B`

C

`(3)/(2) A + (7)/(3) B`

D

`(A)/(2) + (B)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
3
`v = (ds)/(dt) = At + Bt^(2)`
`int_(0)^(s) ds = int_(1)^(s) (At + Bt^(2)) dt`
`s = (A)/(2) |(|t^(2)|_(1)^(2)) + (B)/(3) (|t^(3)|_(1)^(2))|`
`= (A)/(2) (2^(2) - 1^(2)) + (B)/(3) (2^(3) - 1^(3))`
`= (3 A)/(2) + (7 B)/(3)`
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Knowledge Check

  • If the velocity of a particle is v=At+Bt^(2) , where A and B are constants, then the distance travelled by it between 1 s and 2 s is :

    A
    `(3)/(2)A+4B`
    B
    `3A+7B`
    C
    `(3)/(2)A+(7)/(3)B`
    D
    `(A)/(2)+(B)/(3)`

  • the velocity of a particle varies with time as shown below the distance travelled by the travelled by the particle during t=2s"and" t= 6s. Is

    A
    `2pi m`
    B
    `(2pi + 40) m`
    C
    `4pi m`
    D
    `40 m`

  • . If the velocity of a particle is (10 + 2 t 2) m/s , then the average acceleration of the particle between 2s and 5s is

    A
    `2m//s^(2)`
    B
    `4m//s^(2)`
    C
    `12m//s^(2)`
    D
    `14m//s^(2)`

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