Consider a body of mass 2kg at rest at the origin at time t=0. A force (αt^i+β^j) is applied on the body where α=2 Ns−1 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 Ns−1 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.