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The distance travelled by a particle from a fixed point is given as s = (t3 - t2...


Question

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.

Options

A) 2.3 cm

B) 4.0 cm

C) 5.2 cm

D) 6.0 cm

The correct answer is 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

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Dicussion (1)

  • 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

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