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Question

Consider a body of mass 2 kg at rest at the origin at time t=0. A force (αt ^i+β ^j) is applied on the body where α=2 Ns1 and β=2 N. Then, which of the following statement(s) is/are true at t=2 s?

A
The velocity of the body along the direction ^i is 2 m/s.
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B
The velocity of the body along the direction ^j is 2 m/s.
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C
The velocity of the body along the direction ^i is 4 m/s.
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D
The velocity of the body along the direction ^j is 4 m/s.
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Solution

The correct options are
A The velocity of the body along the direction ^i is 2 m/s.
B The velocity of the body along the direction ^j is 2 m/s.
Given that
Mass of the block (m)=2 kg
Force (F)=(αt^i+β^j)
where
α=2 Ns1
β=2 N
F=(αt)^i+β^j
F=2t^i+2^j
mdvdt=2t^i+2^j
On integrating,
v0mdv=t0(2t^i+2^j)dt
[given, body is at rest at t=0]
mv=t2^i+2t^j
v=t2^i+2t^jm
v=t2^i+2t^j2
v=t22^i+t^j
v=2^i+2^j (at t=2sec)
options (a) and (b) are correct.

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