Question

The position x of a particle with respect to time t along x-axis is given by x=9t2t3 where x is in metres and t is in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction?

A
54 m
B
81 m
C
24 m
D
32 m
Solution
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Given that,
x=9t2t3.....(I)
We know that,
v=dxdt
The maximum speed is
v=18t3t2
v maximum, at dvdt=0
dvdt=186t
The time will be
0=186t
t=3 sec
The position of the particle at 3 sec
Put the value of t in equation (I)
x=9×927
x=8127
x=54 m
The position of the particle will be 54 m.
Hence, Option A is correct

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