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Motion in A Straight Line question

2006 · Q153
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Motion in A Straight Line question

2006 · Q153

NEETPhysicsMotion in A Straight LineMCQ+4 / −1
A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t −-− t3. How long would the particle travel before coming to rest ?
  1. A
    16 m
  2. B
    24 m
  3. C
    40 m
  4. D
    56 m
View written solutionFree

Correct answer: A

Given x = 40 + 12t −-− t3

v = dxdt{{dx} \over {dt}}dtdx​ = 12 - 3t2

When particle comes to rest then v = 0.

∴\therefore∴ 12 - 3t2 = 0

⇒\Rightarrow⇒ t = 2 s

Distance travelled before coming to rest,

s = ∫02vdt\int\limits_0^2 {vdt} 0∫2​vdt = ∫02(12−3t2)dt\int\limits_0^2 {\left( {12 - 3{t^2}} \right)dt} 0∫2​(12−3t2)dt

= [12t−3t33]02{\left[ {12t - {{3{t^3}} \over 3}} \right]_0^2}[12t−33t3​]02​

= 24 - 8 = 16 m

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