Home
Class 11
PHYSICS
A particle A of mass 10//7kg is moving i...

A particle A of mass `10//7kg` is moving in the positive direction of `x-axis`. At initial position `x=0`, its velocity is `1ms^-1`, then its velocity at `x=10m` is (use the graph given)

A

(a) `4ms^-1`

B

(b) `2ms^-1`

C

(c) `3sqrt2ms^-1`

D

(d) `100/3ms^-1`

Text Solution

Verified by Experts

The correct Answer is:
A
Area under `P-x` graph
`=int pdx=(m(dv)/(dt))vdx=underset1oversetvintmv^2dV`
`=[(mv^3)/(3)]_1^v=(10)/(7xx3)(v^3-1)`
From the graph, `area=1/2(2+4)xx10=30`
or `(10)/(7xx3)(v^3-1)=30`
or `v=4ms^-1`
Alternative method:
From graph
`P=0.2x+2`
`mv(dv)/(dx)v=0.2x+2`
`mv^2dv=(0.2x+2)dx`
Now integrating both sides, we get
`underset1oversetvintmv^2dv=underset0overset10int(0.2x+2)dx`
`v=4ms^-1`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • WORK, POWER & ENERGY

    CENGAGE PHYSICS|Exercise Multiple Correct|25 Videos

  • WORK, POWER & ENERGY

    CENGAGE PHYSICS|Exercise Linked Comprehension|55 Videos

  • WORK, POWER & ENERGY

    CENGAGE PHYSICS|Exercise Subjective|23 Videos

  • VECTORS

    CENGAGE PHYSICS|Exercise Exercise Multiple Correct|5 Videos

Similar Questions

Explore conceptually related problems

7.A particle A of mass 10/7kg is moving in the positive direction of x .Its initial position is x=0 & initial velocity is 1m/s .The velocity at x=10 is: (use the graph given)

A particle of mass 10^-2kg is moving along the positive x axis under the influence of a force F(x)=-K//(2x^2) where K=10^-2Nm^2 . At time t=0 it is at x=1.0m and its velocity is v=0 . (a) Find its velocity when it reaches x=0.50m . (b) Find the time at which it reaches x=0.25m .

Knowledge Check

  • A particle is moving on a straight line with constant retardation of 1 m//s^(2) . Its initial velocity is 10 m//s .

    A
    The distance travelled by the particle till it comes to rest is 50 m.
    B
    The average velocity till it comes to rest is `5 m//s`.
    C
    It comes to rest in 5 sec.
    D
    Its velocity after 5 sec is `5 m//s`

  • The velocity of a particle moving in the positive direction of x-axis veries as v=10sqrtx . Assuming that at t=0 , particle was at x=0

    A
    The initial velocity of the particle is zero
    B
    the initial velocity of the particle is `2.5(m)/(s)`.
    C
    The accelration of the particle is `2.5(m)/(s^2)`.
    D
    The acceleration of the particle is `50(m)/(s^2)`.

  • A particle of mass 10^31 kg is moving with a velocity equal to 10^5ms^-1 . The wavelength of the particle is equal to

    A
    0
    B
    `6.6xx10^-8m`
    C
    0.66m
    D
    `1.5xx10^7m`

    • Similar Questions

    Explore conceptually related problems

    A particle is moving along x-direction with a constant acceleration a. The particle starts from x=x_0 position with initial velocity u. We can define the position of the particle with time by the relation x=x_0+ut+(1)/(2)at^2 plot the position of the particle in relation with time is following situations (i) If initial position of the particle is on negativ x-axis, initial velocity is positive and acceleration is negative. (ii) If initial position is positive, initial velocity is negative and acceleration is positive.

    A particle starts from rest at the origin and moves along the positive x direction. Its acceleration a versus position x graph is shown in the figure. The velocity of the particle at x = 6 m is?

    A particle moving in the positive x-direction has initial velocity v_(0) . The particle undergoes retardation kv^(2) , where vis its instantaneous velocity. The velocity of the particle as a function of time is given by:

    A particle moving in the positive x-direction has initial velocity v_(0) . The particle undergoes retardation kv^(2) , where v is its instantaneous velocity. The velocity of the particle as a function of time is given by

    At the moment t=0 particle leaves the origin and moves in the positive direction of the x-axis. Its velocity varies with time as v=10(1-t//5) . The dislpacement and distance in 8 second will be

    Home
    Profile