A particle moves along x-axis and its displacement
at any time is given by
3 2 x(t) 2t 3t 4t
in SI
units. The velocity of the particle when its
acceleration is zero, is:
(a)
1
2.5 ms
(b)
1
3.5 ms
(c)
1
4.5 ms
(d)
1
8.5 m
Answers
Answered by
23
ANSWER
Displacement of the particle x(t)=2t
3
−3t
2
+4t m
Thus velocity of particle v(t)=
dt
d
x(t)=6t
2
−6t+4 m/s
Acceleration of particle a(t)=
dt
d
v(t)=12t−6 m/s
2
Let acceleration is zero at the instant t
o
i.e. a(t
o
)=0
∴ 12t
o
−6=0 ⟹t
o
=0.5 s
Thus velocity at the instant t
o
, v(t
o
)=6(0.5)
2
−6(0.5)+4=2.5 m/s
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