Home
Class 11
PHYSICS
Velocity of particle moving along positi...

Velocity of particle moving along positive x-direction is `v = (40-10t)m//s`. Here,t is in seconds. At time `t=0,` tha x coordinate of particle is zero. Find the time when the particle is at a distance of 60 m from origin.

A

`t_3=2(1+sqrt7)s`

B

`t_3=2(2+sqrt7)s`

C

`t_3=2(2+sqrt9)s`

D

`t_3=sqrt7)s`

Text Solution

Verified by Experts

The correct Answer is:
B

Comparing with `v=u+at,` we have,
`u=40m//s` and `a=-10m//s^2`

Distance of 60m from origin may be at `x=+60m`
and `x=-60 m`.
From the figure, we can see that at these two points
particle is at three times `t_1,t_2` and `t_3.`
For `X=+60m` or `t_1` and `t_2`
`s=ut+1/2at^2`
`rArr 60=(+40)t+1/2(-10)t^2`
Solving this equation, we get
`t_1=2s` and `t_2=6s`
For `X-60m` or `t_3`
`s=ut+1/2at^2`
Solving this equation, we get positive value of t as
`t_3=2(2+sqrt7)s`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • KINEMATICS

    DC PANDEY|Exercise More Than One Correct|6 Videos
  • KINEMATICS

    DC PANDEY|Exercise Comprehension|7 Videos
  • KINEMATICS

    DC PANDEY|Exercise Objective|45 Videos
  • GRAVITATION

    DC PANDEY|Exercise (C) Chapter Exercises|45 Videos
  • KINEMATICS 1

    DC PANDEY|Exercise INTEGER_TYPE|15 Videos

Similar Questions

Explore conceptually related problems

Find the time t_0 when x-coordinate of the particle is zero.

Velocity (in m/s) of a particle moving along x-axis varies with time as, v= (10+ 5t -t^2) At time t=0, x=0. Find (a) acceleration of particle at t = 2 s and (b) x-coordinate of particle at t=3s

Knowledge Check

  • A particle moving along the x axis has a position given by x=54 t - 2.0 t^(3) m . At the time t=3.0s , the speed of the particle is zero. Which statement is correct ?

    A
    `4.3xx10^(4) m//s^(2)`, south
    B
    `9.4 xx10^(4)m//s^(2)`, north
    C
    `5.1xx10^(4)m//s^(2)`, north
    D
    `2.2 xx 10^(3) m//s^(2)`, south
  • Velocity v of a particle moving along x axis as a function of time is given by v = 2t m//s . Initially the particle is to the right of the origin and 2 m away from it. Find the position (distance from origin) of the particle after first 3 s .

    A
    5 m
    B
    7 m
    C
    11 m
    D
    9 m
  • v_(x) is the velocity of a particle moving along the x-axis as shown in the figure. If x=2.0m at t=1.0s, what is the position of the particle at t=6.0s ?

    A
    `-2.0` m
    B
    `+2.0` m
    C
    `+1.0` m
    D
    `-1.0` m
  • Similar Questions

    Explore conceptually related problems

    A particle is moving along x-axis. At time t=0, Its x-coordinate is x=-4 m. Its velocity-time equation is v=8-2t where, v is in m//s and t in seconds. (a) At how many times, particle is at a distance of 8m from the origin? (b) Find those times.

    At the moment t=0 a particle leaves the origin and moves in the positive direction of the x-axis. Its velocity varies with time as v=v_0(1-t//tau) , where v_0 is the initial velocity vector whose modulus equals v_0=10.0cm//s , tau=5.0s . Find: (a) the x coordinate of the particle at the moments of time 6.0 , 10 , and 20s , (b) the moments of time when the particles is at the distance 10.0cm from the origion, (c) the distance s covered by the particle during the first 4.0 and 8.0s , draw the approximate plot s(t) .

    A particle moves along the x-axis obeying the equation x=t(t-1)(t-2) , where x is in meter and t is in second a. Find the initial velocity of the particle. b. Find the initial acceleration of the particle. c. Find the time when the displacement of the particle is zero. d. Find the displacement when the velocity of the particle is zero. e. Find the acceleration of the particle when its velocity is zero.

    [" Velocity of a particle moving along "x" -axis "],[" as a function of time is given as "v=(4-],[t^(2))m/s," where "t" is time in second.The "],[" displacement of particle during "t=0s" to "t],[=1s" is "]

    A particle is moving along positive X direction and is retarding uniformly. The particle crosses the origin at time t = 0 and crosses the point x = 4.0 m at t = 2 s . (a) Find the maximum speed that the particle can possess at x = 0 . (b) Find the maximum value of retardation that the particle can have.