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The displacement, S metres of a moving particle from point O, after t seconds is given by:
S = t3 – 5t2 + 3t + 10

  1. Find S when t = 2 
  2. Determine:
    • The velocity of the particle when t = 5sec 
    • The value of t when the particles is momentarily at rest.
  3. Find the time, when the velocity of the particle is maximum.

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  1. Find S when t = 2 
    When t = 2
    S = (2)3 – 5(2)2 + 3(2) + 10
    8 – 20 + 6 + 10
    = 4m
  2. Determine:
    • The velocity of the particle when t = 5sec 
      V = ds/dt = 3t2 – 10t + 3
      When t = 5
      V = 3(5)2 – 10(5) + 3
      75 – 50 + 3
      = 28 m/s
    • The value of t when the particles is momentarily at rest .
      Momentarily at rest V = 0
      3t2 – 10t + 3 = 0
      3t2 – 9t – t + 3 = 0
      3t(t – 3) 1(t – 3) = 0
      (3t – 1) (t – 3) = 0
      Either
      3t – 1 = 0 → t = 1/3sec
      Or t – 3 = 0 → t = 3 sec
  3. Find the time, when the velocity of the particle is maximum. 
    Velocity maximum dvdt=0
    6t – 10 = 0
    6t = 10
    t = 106 =53 seconds
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