The distance travelled by a particle from a fixed point is given as s =…

The distance travelled by a particle from a fixed point is given as s = (t³ – t² – t + 5)cm. Find the minimum distance that the particle can cover from the fixed point.

Correct Answer: Option C

Explanation

S = t³ – t² – t + 5^ds/_dt = 3t² – 2t – 1
As ds = 0
3t² – 2t – 1 = 0
(3t+1)(t-1) = 0
∴ t = 1 or –¹/₃
At min pt t = –¹/₃
S = t³ – t² – t + 5 put t = –¹/₃
= (-¹/₃)³ – (-¹/₃)² – (-¹/₃) + 5
= –¹/₂₇ – ¹/₉ + ¹/₃ + 5
= 140 / 27
= 5.2