QNEET-2024-Ph-155: NEET 2024 Physics - Class 11 NEET-2024-Ph-155 Solution: An object moving along horizontal x-direction with kinetic…

To find the kinetic energy of the object at the end of the displacement, we need to calculate the work done by the force F _ on the object during its displacement. The work done by a force is given by the dot product of the force and the displacement vectors: W = F _ _ d _ Here, the force F _ is given as: F _ = _ 2 i ^ + 3 j ^ N And the displacement d _ is given as: d _ = 3 i ^ m The dot product of the two vectors is calculated as follows: W = ( _ 2 i ^ + 3 j ^ ) _ ( 3 i ^ ) Since the j ^ component of the force does not contribute to the work done in the x -direction, it can be ignored. Thus, the dot product yields: W = _ 2 _ 3 N _ m = _ 6 J The negative sign indicates that the force does work against the direction of displacement. Now, the initial kinetic energy of the object is: K i = 10 J The work-energy theorem relates the work done on an object to its change in kinetic energy: W = K f _ K i Rearranging for the final kinetic energy K f gives: K f = K i + W Substituting the known values: K f = 10 J + ( _ 6 J ) This simplifies to: K f = 4 J Hence, the kinetic energy of the object at the end of the displacement is Option C: 4   J .