The distance traveled by a particle from a fixed point is given as s = (t $^3$ - t $^2$ - t + 5)cm. Find the minimum distance that the particle can cover from the fixed point?

2.3 cm

4.0 cm

5.2 cm

6.0 cm

Correct answer is B

S = t $^3$ - t $^2$ - t + 5
ds/dt = 3t $^2$ - 2t - 1
As ds = 0
3t $^2$ - 2t - 1 = 0
(3t+1)(t-1) = 0
∴ t = 1 or -1/3
At min pt t = 1
S = t $^3$ - t $^2$ - t + 5

put t = 1
= 1 $^3$ - \1(^2\) - 1 + 5
= 1 - 1 - 1 + 5

= 4

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