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A particle is moving along x-axis. At ti...

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.

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
(a) Comparing the given v-t equation with `v=u+at.` we have,
`u=8 m//s` and
`a=-2 m//s^2=constant`
Now, motion of the particle is as shown below.
Now, `8m` distance from origin will be at two coordinates `x=8m and x=-8m.` From the diagram, we can see that particle will cross these two points three times, `t_1,t_2,and t_3.`
(b) `t_1` and `t_2`: At `x=8 m` displacement from the strating point is
`s=x_f-x_i=8-(4)=12 m`
Substituting in `s=ut+1/2 at^2,` we have
`12=8t-1/2xx2xxt^2`
Solving this equation, we get
smaller time `t_1=2s`
and larger time `t_2=6s`
`t_3`: At `x=-8m,` displacement from the starting point is
`s=x_f-x_i=-8-(-4)=-4 m`
Substituting in `s=ut+1/2at^2,` we have `-4=8t-1/2xx2xxt^2`
Solving this equation, we get the positive time,
`t_3=8.47s`
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Knowledge Check

  • A particle is travelling along X-axis and its x-coordinate is related to time as follows: x=5t^(2)-20 Here x is measured in metres and time t in seconds. When does the particle cross the origin?

    A
    2s
    B
    3s
    C
    1s
    D
    never

  • A particle is moving along X-axis Its acceleration at time t is proportional to its velocity at that time. The differential equation of the motion of the particle is

    A
    `(d^(2)x)/(dt^(2))-k(dx)/(dt)=0,kgt0`
    B
    `(d^(2)x)/(dt^(2))+k(dx)/(dt)=0,kgt0`
    C
    `(d^(2)x)/(dt^(2))-k=0,kgt0`
    D
    `(d^(2)x)/(dt^(2))+k=0,kgt0`

  • The motion of a particle moving along x-axis is represented by the equation (dv)/(dt)=6-3v , where v is in m/s and t is in second. If the particle is at rest at t = 0 , then

    A
    The speed of the particle in 2 /s when the acceleration of particle is zero
    B
    After a long time the particle moves with a constant velocity of 2 m/s
    C
    The speed is 0.1 m/s, when the acceleration is half of its initial value
    D
    The magnitude of final acceleration is `6m//s^(2)`