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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

Grade:10

## 2 Answers

Jitender Pal
askIITians Faculty 365 Points
7 years ago

(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

sharath kumar
35 Points
7 years ago

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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