The position x of a particle with respect to time t along x-axis is given by x = 9t² – t³ where x is in metres and t in second. What will be the position of this particle when it achieves maximum speed along the +ve x direction?

Options

(a) 54 m
(b) 81 m
(c) 24 m
(d) 32 m

Correct Answer:

54 m

Explanation:

Speed v = dx/ dt = d/ dt (9t² – t³) = 18t – 3t² For maximum speed
dv/ dt = 0 ⇒ 18 – 6t = 0 ⇒ t= 3
⇒Xmax = 81 – 27 = 54