Question

The position `x` of a particle with respect to time `t` along the x-axis is given by `x=9t^(2)-t^(3)` where `x` is in meter and `t` in second. What will be the position of this particle when it achieves maximum speed along the positive `x` direction
A. 32 m
B. 54 m
C. 81 m
D. 24 m

Answer 1

Correct Answer - B
`x=9t^(2)-t^(3)`
`v=(dx)/(dt)=18t-3t^(2)`
`a=(dv)/(dt)=18-6t`
When` v` is maximum, `a=(dv)/(dt)=0`
`18-6t=0impliest=3s`
At `t=3 s, x=9(3)^(2)-(3)^(3)=54 m`