A block of mass 2 kg F ( t ) ↑ is free to move along the x -axis. It is at rest and from t = 0 onwards it is subjected to a timedependent force F ( t ) in the x direction. The force F ( t ) varies wit

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A block of mass 2 kg F ( t ) ↑ is free to move along the x -axis. It is at rest and from t = 0 onwards it is subjected to a timedependent force F ( t ) in the x direction. The force F ( t ) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is

TestHub · Accepted Answer

Change in momentum = area under F - t graph Δ p ​ = 2 1 ​ × 4 × 3 − 2 1 ​ × 1.5 × 3 4 ​ × 1.5 [ Force at 4.5 s = 3 4 ​ × 1.5 N ] = 6 − 1.5 = 4.5 kg m s ​ As Δ p = m ( v − u ) = m v ( ∵ u = 0 ) ∴ v = m Δ p ​ = 2 kg 4.5 kg m s − 1 ​ = 2 4.5 ​ ms − 1 Kinetic energy of the block after 4.5 s is K = 2 1 ​ m v 2 = 2 1 ​ × 2 kg × ( 2 4.5 ​ ms − 1 ) 2 = 5.06 J

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