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A particle is travelling among a straight line OX. The distance x in meters of the particle from O at a time t is given by X = 37 + 27t t³ where t is given by X in the seconds. The distance of particles from O when it comes to rest is W3.
  1. 101m
  2. 81m
  3. 91m
  4. None of these
Explanation

Step 1: Interpret the equation
The given equation is:

x=37+27t−t3

(It seems from the text “X = 37 + 27t t³” likely means X=37+27t−t3 because otherwise it wouldn’t make physical sense for motion.)

Step 2: Find when the particle comes to rest
Velocity v=dxdt=27−3t2.
Set v=0:

27−3t2=0t2=9t=3 s(time positive)

Step 3: Find position at t=3

x=37+27(3)−(3)3x=37+81−27x=91 m

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