Home
Class 12
PHYSICS
A particle moves on the xy-pane such tha...

A particle moves on the xy-pane such that its position vector is given by `vec(r)=3t^(2) hati-t^(3) hatj`. The equation of trajectory of the particle is given by

A

`3x^(2)+16 y =0`

B

`((3x)/2)^(4//3)+4y=0`

C

`(x/32)^(3//2) +y=0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
3
`vec(r)=2t^(2) hati-t^(3) hatj`
`x=2t^(3) " " y=-t^(3)`
`(x/2)^(1//2)=t" " y=-(x/2)^(3//2)`
`(x/2)^(3//2) +y=0`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • TEST PAPERS

    BANSAL|Exercise PHYSICS PART (A)|32 Videos

  • TEST PAPERS

    BANSAL|Exercise PHYSICS PART (B)|3 Videos

  • TEST PAPERS

    BANSAL|Exercise PHYSICS PART- C|4 Videos

  • SEMICONDUCTORS

    BANSAL|Exercise CBSE Question|32 Videos

Similar Questions

Explore conceptually related problems

The position of a particle is given as vecr=at hati+bt^(2)hatj Find the equation of trajectory of the particle.

A particle move in x-y plane such that its position vector varies with time as vec r=(2 sin 3t)hat j+2 (1-cos 3 t) hat j . Find the equation of the trajectory of the particle.

Knowledge Check

  • A particle of mass 2 kg is moving such that at time t, its position, in meter, is given by vecr(t)=5hati-2t^(2)hatj . The angular momentum of the particle at t = 2s about the origin in kg m^(-2)s^(-1) is :

    A
    `-80hatk`
    B
    `(10hati-16hatj)`
    C
    `-40hatk`
    D
    `40hatk`

  • A particle moves in space such that its position vector varies as vec(r)=2thati+3t^(2)hatj . If mass of particle is 2 kg then angular momentum of particle about origin at t=2 sec is

    A
    `12hatk`
    B
    `48hatk`
    C
    `36hatk`
    D
    `24hatk`

  • A particle moves in xy-plane. The position vector of particle at any time is vecr={(2t)hati+(2t^(2))hatj}m. The rate of change of theta at time t = 2 second. ( where 0 is the angle which its velocity vector makes with positive x-axis) is :

    A
    `2/(17) "rad"//s`
    B
    `1/(14)"rad"//s`
    C
    `4/7 "rad"//s`
    D
    `6/5"rad"//s`

    • Similar Questions

    Explore conceptually related problems

    The position vector of a particle moving in x-y plane is given by vec(r)=(t^(2)-4)hat(i)+(t-4)hat(j) . Find (a) Equation of trajectory of the particle (b)Time when it crosses x-axis and y-axis

    A particle moves along the x-axis so that its position is given x = 2t^(3) –3t^(2) at a time t second. What is the time interval duringwhich particle will be on the negative half of the axis?

    A particle moves along a straight line such that its displacement at any time t is given by s = 3t^(3)+7t^(2)+14t + 5 . The acceleration of the particle at t = 1s is

    The position of a particle is given by vec(r) = 3that(i) - 4t^(2)hat(j) + 5hat(k). Then the magnitude of the velocity of the particle at t = 2 s is

    A particle moves in x-y plane. The position vector of particle at any time t is vecr={(2t)hati+(2t^2)hatj} m. The rate of change of theta at time t = 2 s (where theta is the angle which its velocity vector makes with positive x-axis) is

    Home
    Profile