2009
Mathematics
67ca00ce0c643c71d77dee1f
The distance traveled 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?
A.
2.3 cm
B.
4.0 cm
C.
5.2 cm
D.
6.0 cm
Correct Answer: 4.0 cm
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 S = t3 - t2 - t + 5 put t = 1 = 13 - 12 - 1 + 5 = 1 - 1 - 1 + 5 = 4
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 S = t3 - t2 - t + 5 put t = 1 = 13 - 12 - 1 + 5 = 1 - 1 - 1 + 5 = 4THIS WEEK's
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