Question

The position x of a particle with respect to time t
along x-axis is given by x = 92 - p, where x is in
metres and t in second. What will be the position
of this particle when it achieves maximum speed
along the positive x-direction?​

Answer 1

Answer:

54m

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Answer 2

Given that,

x=9t

2

−t

3

.....(I)

We know that,

v=

dt

dx

The maximum speed is

v=18t−3t

2

v maximum, at

dt

dv

=0

dt

dv

=18−6t

The time will be

0=18−6t

t=3 sec

The position of the particle at 3 sec

Put the value of t in equation (I)

x=9×9−27

x=81−27

x=54 m

The position of the particle will be 54 m.