Home
Class 11
PHYSICS
The displacement of a particle is given ...

The displacement of a particle is given by `x=(t-2)^(2)` where x is in meter and t in second. The distance covered by the particle in first 3 seconds is

A

4 m

B

8 m

C

12 m

D

16 m

Text Solution

Verified by Experts

The correct Answer is:
D
Given , `x = (t-2)^(2)`
Velocity, `v = (dx)/(dt) = (d)/(dt) (t-2)^(2) =2(t-2) m//s`
Acceleration, `a = (dv)/(dt) = (d)/(dt) [2(t-2)]`
`= 2 [1-0] = 2 m//s^(2)`
When `t = 0, v = - 4 m//s`
`t = 2s, v = 0 m//s`
`t = 4s, v = 4 m//s`
`v -t` graph is shown in adjacent diagram,
Distance travelled `=` area of the graph
`=` area of `OAC +` area ABD
`= (4 xx 2)/(2) + 1/2 xx 2 xx 4 = 8m`
Promotional Banner

Topper's Solved these Questions

  • MOTION IN A STRAIGHT LINE

    NCERT EXEMPLAR|Exercise Multiple Choice Question (More Than One Qns)|6 Videos

  • MOTION IN A STRAIGHT LINE

    NCERT EXEMPLAR|Exercise Very Short Answer Type Qns|14 Videos

  • MOTION IN A PLANE

    NCERT EXEMPLAR|Exercise Multiple Choice Questions|37 Videos

  • OSCILLATIONS

    NCERT EXEMPLAR|Exercise MULTIPLE CHOICE QUESTIONS (MCQs)|40 Videos

Similar Questions

Explore conceptually related problems

The displacement of a partcle is given by x=(t-2)^(2) where x is in metre and t in second. The distance coverred by the particle in first 3 seconds is

The displacement of a particle is moving by x = (t - 2)^2 where x is in metres and t in second. The distance covered by the particle in first 4 seconds is.

The x -coordinate of a particle moving along x -axis varies with time as x=6-4t+t^(2), where x in meter and t in second then distance covered by the particle in first 3 seconds is

The position x of a particle varies with time t as x = 6 + 12t - 2 t^2 where x is in metre and in seconds. The distance travelled by the particle in first five seconds is

The displacement of a particle is given by y=(6t^2+3t+4)m , where t is in seconds. Calculate the instantaneous speed of the particle.

The displacement of a particle moving in a straight line is described by the relation s=6+12t-2t^(2) . Here s is in metre and t in second. The distance covered by the particle in first 5s is

Under the action of a force, a 2 kg body moves such that its position x as a function of time is given by x =(t^(3))/(3) where x is in meter and t in second. The work done by the force in the first two seconds is .

The position of a particle is given by x=2(t-t^(2)) where t is expressed in seconds and x is in metre. The particle

A force acts on a 3.0 gm particle in such a way that the position of the particle as a function of time is given by x=3t-4t^(2)+t^(3) , where xx is in metres and t is in seconds. The work done during the first 4 seconds is