Mathematics

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.
  • A.
    2.3 cm
  • B.
    4.0 cm
  • C.
    5.2 cm
  • D.
    6.0 cm
Correct Answer: Option C
Explanation

S = t3 – t2 – t + 5ds/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
= –1/271/9 + 1/3 + 5
= 140 / 27
= 5.2