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A particle starts moving rectilinearly a...

A particle starts moving rectilinearly at time `t=0` such that its velocity `v` changes with time `t` according to the equation `v=t^(2)-t`, where `t` is in seconds and `v` in `ms^(-1)`. Find the time interval for which the particle retards.

A

`(1)/(2) lt t lt 1`

B

`(1)/(2) gt t gt1`

C

`(1)/(4) lt t lt 1`

D

`(1)/(2) lt t lt(3)/(4)`

Text Solution

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Knowledge Check

  • A particle starts moving rectilinearly at time t = 0 such that its velocity v changes with time t according to the equation v = t^2-t , where t is in seconds and v is in m s^(-1) . The time interval for which the particle retrads (i.e., magnitude of velocity decreases)is

    A
    `t lt 1//2`
    B
    `1//2 ltt lt1`
    C
    `tgt1`
    D
    `tlt1//2 and tgt1`

  • A particle starts moving rectillineraly at time t = 0 , such that its velocity 'v' changes with time 't' according to the equation v = t^(2) -t where t is in seconds and v is in m//s . The time interval for which the particle retards is

    A
    `t lt 1//2`
    B
    `1//2 lt tlt 1`
    C
    `t gt 1`
    D
    `t lt 1//2` and `t gt 1`

  • Velocity of a particle of mass 2kg varies with time t according to the equation vec(v)=(2thati+4hatj) m//s . Here t is in seconds. Find the impulse imparted to the particle in the time interval from t=0 to t=2s.

    A
    `2hati m//s`
    B
    `4hati m//s`
    C
    `8hati m//s`
    D
    `6hatim//s`
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