A particle is moving along a straight line and it position is given by x = t 3 – t 2 + 1 velocity is given by 
and acceleration is given by 
(i) Velocity of the particle at t = 2s is-
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Ans.
(i)
Sol. x = t 3 – t 2 + 1
= 3t 2 – 2t
at t = 2s, 
= 3 × 2 2 – 2 × 2 = 8 m/s
= 6t – 2
at t = 1s, 
= 6 × 1 – 2 = 4 m/s 2 
= 0 ⇒ 6t – 2 = 0, t = 
s
(ii)
Sol. x = t
3 – t 2 + 1
= 3t 2 – 2t
at t = 2s, 
= 3 × 2 2 – 2 × 2 = 8 m/s
= 6t – 2
at t = 1s, 
= 6 × 1 – 2 = 4 m/s 2 
= 0 ⇒ 6t – 2 = 0, t = 
s
(iii)
Sol. x = t
3 – t 2 + 1
= 3t 2 – 2t
at t = 2s, 
= 3 × 2 2 – 2 × 2 = 8 m/s
= 6t – 2
at t = 1s, 
= 6 × 1 – 2 = 4 m/s 2 
= 0 ⇒ 6t – 2 = 0, t = 
s
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