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Motion in A Straight Line question

2013 · Q145
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Motion in A Straight Line question

2013 · Q145

NEETPhysicsMotion in A Straight LineMCQ+4 / −1
The displacement 'x' (in meter) of a particle of mass 'm' (in kg) moving in one dimension under the action of a force, is related to time 't' (in sec) by t = x+3\sqrt x + 3x​+3. The displacement of the particle when its velocity is zero, will be
  1. A
    4 m
  2. B
    0 m (zero)
  3. C
    6 m
  4. D
    2 m
View written solutionFree

Correct answer: B

As t = x+3\sqrt x + 3x​+3

⇒\Rightarrow⇒ x=t−3\sqrt x = t - 3x​=t−3

⇒\Rightarrow⇒ x=(t−3)2x = {\left( {t - 3} \right)^2}x=(t−3)2

Velocity, v = dxdt{{dx} \over {dt}}dtdx​ = 2(t−3t - 3t−3)

Velocity of the particle becomes zero, when

2(t−3t - 3t−3) = 0 ⇒\Rightarrow⇒ t = 3 s

At t = 3 s,

x=(3−3)2x = {\left( {3 - 3} \right)^2}x=(3−3)2 = 0 m

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