Home
Class 11
PHYSICS
For the one dimensional motion, describe...

For the one dimensional motion, described by `x=t-sint`

A

`x(t)gt0` for all `tgt0`

B

`v(t)gt0` for all `tgt0`

C

`a(t)gt0` for all `tgt0`

D

`v(t)` lies between 0 and 2

Text Solution

Verified by Experts

The correct Answer is:
A, D
`x=t-sint`
velocity `v=(dx)/(dt)=(d)/(dt)[t-sint]`
`=1-cost`
Acceleration `a=(dv)/(dt)=(d)/(dt)[1-cost]=sint`
As acceleration `agt0` for all `tgt0`
Hence, `x(t)gt0` for all `tgt0`
velocity `v=1-cost`
When `cost=1` velocity `v=0`
`V_(max)=1-(cost)_(min)=1-(-1)=2`
`V_(min)=1-(cost)_(max)=1-1=0`
Hence, v lies between 0 and 2.
Acceleration `a=(dv)/(dt)=-sint`
When `t=0,x=0,x=+1,a=0`
When `t=(pi)/(2),x=1,v=0,a=-1`
`t=pi,x=0,x=-1,a=1`
When `t=2pi,x=0,x=0,a=0`
Promotional Banner

Topper's Solved these Questions

  • MOTION IN A STRAIGHT LINE

    NARAYNA|Exercise Passage Type Questions|16 Videos

  • MOTION IN A STRAIGHT LINE

    NARAYNA|Exercise Multiple Answer Question|22 Videos

  • MOTION IN A STRAIGHT LINE

    NARAYNA|Exercise Single Type Question|23 Videos

  • MOTION IN A PLANE

    NARAYNA|Exercise Level-II(H.W)|31 Videos

  • NEWTONS LAWS OF MOTION

    NARAYNA|Exercise PASSAGE TYPE QUESTION|6 Videos

Similar Questions

Explore conceptually related problems

The motion of a particle executing SHM in one dimension is described by x = -0.5 sin(2 t + pi//4) where x is in meters and t in seconds. The frequency of oscillation in Hz is

For a particle in one dimensional motion, the instantaeous speed is always equal to the magnitude of instantaneous velocity. Why ?

Force on a particle in one-dimensional motion is given by F=Av+Bt+(Cx)/(At+D) , where F= force, v= speed, t= time, x= position and A, B, C and D are constants. Dimension of C will be-

In the one-dimensional motion of a particle, the relation between position x and time t is given by x^(2)+2x=t (here xgt0 ). Choose the correct statement

A body in one dimensional motion has zero speed at an instant. At that instant, it must have

Figure gives the x-t plot of a particle is one dimensional motion. Give the signs of position, velocity and acceleration of the particle at t = 0.3s

Which of the following graphs cannot represent one dimensional motion of a particle?

Can a prticle in one- dimensional motion have zero speed and a non-zero velocity ?

The velocity-time graph of a particle in one-dimensional motion is shown in the figure. Which of the following formulae is correct for describing the motion of the particle over the time interval t_1 to t_2 ?