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Question

The position of particle travelling along x-axis is given by xt=t39t2+6t where xt is in cm and t is in second. Then–

A
The body comes to rest first at (37)s and then at (3+7)s
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B
The total displacement of the particle in travelling from the first zero of velocity to the second zero of velocity is zero
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C
The total displacement of the particle in travelling from the first zero of the velocity to the second zero of velocity is 74 cm
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D
The particle reverses it’s velocity at (37)s and then at (3+7)s and has a negative velocity for (37)s<t<(3+7)s
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Solution

The correct option is D The particle reverses it’s velocity at (37)s and then at (3+7)s and has a negative velocity for (37)s<t<(3+7)s
xt=t39t2+6t
v=dxtdt=(3t2+18t+6) cms1
for v=0 t=(3±7)s
t1=(37)s and t2=(3+7)s
Displacement of particle between t1 and t2 is
xt2xt1
=((3+7)39(3+7)2+6(3+7))((37)39(37)2+6(37))=74
v<0 for (37)<t<(3+7)

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