Home
Class 11
PHYSICS
A particle starts moving rectilinearly a...

A particle starts moving rectilinearly at time `t = 0` such that its velocity(v) changes with time (t) as per equation –
`v = (t2 – 2t) m//s` for `0 lt t lt 2 s`
`= (–t^(2) + 6t – 8) m//s` for `2 le te 4 s`
(a) Find the interval of time between `t = 0` and `t = 4 s` when particle is retarding.
(b) Find the maximum speed of the particle in the interval `0 le t le 4 s`.

Text Solution

Verified by Experts

The correct Answer is:
(a) `1 lt t lt 2s` and `3 lt t lt 4s` (b) `1m//s`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

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 s^(-1) . Find the time interval for which the particle retards.

A partical is moving in a straight line such that ita velocity is given by v=t^(4)+3t^(2)+8 m//s . Find acceleration at time t=1 s .

Knowledge Check

  • 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`

  • 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 is moving with a velocity of v=(3+ 6t +9t^2) m/s . Find out (a) the acceleration of the particle at t=3 s. (b) the displacement of the particle in the interval t=5s to t=8 s.

    A
    `60`
    B
    `20`
    C
    `10`
    D
    `15`

    • Similar Questions

    Explore conceptually related problems

    Suppose that a particle mvoes on a straight line so that is velocity at time t is v(t)=(t^(2)-2t)m//s . (a). Find the displacement of the particle during the time interval 0 le t le 3 (b). Find the distance traveled by the particle during the time interval 0 le t le 3 .

    A particle is moving along x-axis such that its velocity varies with time according to v=(3m//s^(2))t-(2m//s^(3))t^(2) . Find the velocity at t = 1 s and average velocity of the particle for the interval t = 0 to t = 5 s.

    Find the average velocity of a particle moving along a straight line such that its velocity changes with time as v (m//s) = 4 sin. (pi)/(2) t , over the time interval t = 0 to t = (2n - 1) 2 seconds. (n being any + ve integer).

    If displacement S at time t is S=10t-5t^(2) , then velocity at time t is

    A particle is moving on a straight line. Its velocity at time t is (8-2t)m//s . What is the total distance covered from t=0 to t=6s ?

    Home
    Profile