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Question

A particle moves along X-axis and its displacement at any time is given by x(t)=2t3−3t2+4t in SI units. The velocity of the particle when its acceleration is zero, is

A
2.5 ms1
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B
3.5 ms1
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C
4.5 ms1
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D
8.5 ms1
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Solution

The correct option is A 2.5 ms1
Displacement of the particle x(t)=2t33t2+4t m
Thus velocity of particle v(t)=ddtx(t)=6t26t+4 m/s
Acceleration of particle a(t)=ddtv(t)=12t6 m/s2
Let acceleration is zero at the instant to i.e. a(to)=0
12to6=0 to=0.5 s
Thus velocity at the instant to, v(to)=6(0.5)26(0.5)+4=2.5 m/s

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