Question

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.

Answer 1

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

Answer 2

20