1.

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 is in seconds. What will be the position of this pariticle when it achieves maximum speed along the + x direction ?A. 54 mB. 81 mC. 24 mD. 32 m

Answer» Correct Answer - A
Given, `x = 9t^(2) - t^(3)`
Speed, `v = dx/dt = d/dt(9t^(2) - t^(3))= 18t - 3t^(2)`
For maximum speed, `(dv)/(dt) = 0`
`therefore` 0 = 18 - 6t or t = 3 s.
`therefore x_"max" = 9 xx 3^(2) - 3^(3) = 81 - 27 = 54` m


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