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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?
(a) 54 m
(b) 81 m
(c) 24 m
(d) 32 m
(a) Speed v= dx/dt =d/dt (9t^2-t^3 ) =18 t-3t^2 For maximum speed dv/dt=0 => 18 -6t=0 => t=3 x_max =81-27=54
(a)
For maximum speed
Þ
speed (V) = dx/dt =>d(9t2-t3)/dt = 18t-3t2
for maximum or minimum speed put dv/dt = 0 => 18-6t=0
t = 3 =.> position of particle at maximum velocity = 54
option a is correct answer
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