Home
Class 12
PHYSICS
A particle is moving with speed v=b sqrt...

A particle is moving with speed `v=b sqrt(x)` along positive x-axis. Calculate the speed of the particle at time `t= tau` (assume tha the particle is at origin at t= 0).

A

`(b^(2)tau)/(sqrt(2))`

B

`(b^(2)tau)/4`

C

`(b^(2)tau)/2`

D

`b^(2)tau`

Text Solution

Verified by Experts

The correct Answer is:
C
`u=bsqrt(x)`
`implies(dx)/(dt)=bsqrt(x)impliesint_(0)^(x)(dx)/(sqrt(x))=bint_(0)^(1)dt`
`implies2sqrt(x)=bt impliesx=(b^(2)t^(2))/4`
`impliesu=(dx)/(dt)=(b^(2)t)/2implies` velocity at `t=tau` is `v=(b^(2)tau)/2`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RAY OPTICS AND WAVE OPTICS

    VMC MODULES ENGLISH|Exercise IMPECCABLE|58 Videos

  • REVISION TEST-2 JEE

    VMC MODULES ENGLISH|Exercise PHYSICS|25 Videos

Similar Questions

Explore conceptually related problems

A particle is moving in a circle of radius R with constant speed. The time period of the particle is T. In a time t=(T)/(6) Average speed of the particle is ……

A particle is moving along the x-axis whose acceleration is given by a= 3x-4 , where x is the location of the particle. At t = 0, the particle is at rest at x = 4//3m . The distance travelled by the particles in 5 s is

A particle is moving with constant speed v along x - axis in positive direction. Find the angular velocity of the particle about the point (0, b), when position of the particle is (a, 0).

A particle of mass m is moving anticlockwise, in a circle of radius R in x-y plane with centre at (R,0) with a constant speed v_(2) . If is located at point (2R,0) at time t=0 . A man starts moving with a velocity v_(1) along the positive y -axis from origin at t=0 . Calculate the linear momentum of the particle w.r.t. man as a function of time.

A particle is moving in a circle of radius R with constant speed. The time period of the particle is T. In a time t=(T)/(6) Average velocity of the particle is…..

Acceleration of a particle is given by a= 3t^(2)+2t +1 Where t is time . Find (i) its velocity at time t assuming velocity to be 10 m/s at t = 0. (ii) its position at time t assuming that the particle is at origin at t = 0. (iii) What is the average speed of the particle in the duration t = 0 to t = 1s? (iv) What is the average acceleration of the particle in the duration t = 0 to t = 1s?

The velocity of an object is changing with time and relation is given by the following equation. v=2t+3t^(2) Calculate the position of the object from the origin at t = 2 s. Assume particle to be at origin at t = 0

A 4 kg particle is moving along the x- axis under the action of the force F = - ((pi^(2))/(16)) x N At t = 2 sec the particle passes through the origin and t = 10sec , the speed is 4sqrt(2)m//s The amplitude of the motion is

A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is

A particle of mass m, moving in a circular path of radius R with a constant speed v_2 is located at point (2R, 0) at time t = 0 and a man starts moving with a velocity v_0 along the positive y-axis from origin at time t = 0. Calculate the linear momentum of the particle w.r.t. man as a function of time ______________.

Home
Profile