A mass of 1 k g is acted upon by a single force F → = ( 4 i ^ + 4 j ^ ) N . Due to force, mass is displaced from ( 0 , 0 ) to 1 m , 1 m . If initially, the speed of the particle was 2 m s - 1 , its final speed should approximately be

Question

A mass of 1 k g is acted upon by a single force F → = ( 4 i ^ + 4 j ^ ) N . Due to force, mass is displaced from ( 0 , 0 ) to 1 m , 1 m . If initially, the speed of the particle was 2 m s - 1 , its final speed should approximately be, 6 m s - 1, 4.5 m s - 1, 8 m s - 1, 7.2 m s - 1

MARKS App · Accepted Answer

Mass is displaced from (0, 0) to (1, 1). Therefore displacement is, S → = 1 - 0 i ^ + 1 - 0 j ^ S → = i ^ + j ^ m Given force F → = 4 i ^ + 4 j ^ N ∴ Work done by a constant force, W = F → . S → W = 4 i ^ + 4 j ^ . i ^ + j ^ W = 4 + 4 = 8 J From work-energy theorem Δ K = W 1 2 m ν 2 2 - ν 1 2 = W 1 2 1 ν 2 2 - 2 2 = 8 ν 2 2 = 20 ν 2 = 4.5 m s - 1

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