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Question

A body starts from the origin and moves along the X-axis such that the velocity at any instant is given by (4t32t). Where t is in second and velocity is in m/s. What is acceleration of the particle, when it is at distance 2m from the origin.

A
28m/s2
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B
22m/s2
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C
12m/s2
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D
10m/s2
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Solution

The correct option is B 22m/s2
Velocity, V=4t32t , t is in sec.
Displacement dx=vdt
x=(t32t)dt
=tnt2
for x=2m, t=?
tnt22=0
tn2t2+t22=0
t2(t22)+1(t22)=0
t2=2
t=2sec
Acceleration, a=dvdt=12t22
=12(2)2 (t2)
a=22m/s2
Hence, the answer is 22m/s2.


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