The position x of a particle with respect to time t along x-axis is given by x=9t2βt3 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
Medium
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Solution
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Correct option is A)
Given that,
x=9t2βt3.....(I)
We know that,
v=dtdxβ
The maximum speed is
v=18tβ3t2
v maximum, at dtdvβ=0
dtdvβ=18β6t
The time will be
0=18β6t
t=3Β sec
The position of the particle at 3 sec
Put the value of t in equation (I)
x=9Γ9β27
x=81β27
x=54Β m
The position of the particle will be 54Β m.
Hence, Option A is correct
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