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The position x of a particle with respect to time t along x-axis is given by x = 9t 2 - t 3 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



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
8 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
8 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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