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Question

A body starts from origin and moves along x-axis such that at any instant velocity is vt=4t32t where t is in second and vt is in ms1. The acceleration of the particle when it is 2m from the origin is

A
28ms2
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B
22ms2
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C
12ms2
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D
10ms2
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Solution

The correct option is B 22ms2
Given,
vt=4t32t
Acceleration, a=dvtdt
a=12t22. . . . . . . . . . .(1)
displacement, ds=vtdt
20ds=2=(4t32t)dt
t4t2=2
t4t22=0
t2(t22)+1(t22)=0
(t2+1)(t22)=0
t2=2
t=±2
So, t=2
From equation (1),
a=12(2)22
a=242
a=22m/s2
The correct option is B.

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