The position X of a particle with respect to time t along X axis is in meter and t in seconds what will be the position of the particle when it achieves maximum speed along positive X direction
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Answer:
The position x of a particle with respect to time t along x-axis is given by x=9t2−t3 where x is in metres and t is in seconds.
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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.
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.
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