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

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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.

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