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Acceleration doesn't matter in either case.

-- Potential energy of the lifted rock:

PE = M G H = 5 x 9.8 x 5 = 245 joules

-- Kinetic energy of the pushed rock:

KE = 1/2 M V2 = (2.5) (12)2 = 360 joules

The pushed rock requires more work ... 360 joules vs. 245 joules.

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Q: Which requires more work lifting a 5 kg rock to a height of 5 m without accelerating or accelerating the same rock over the same distance horizontally from rest to a speed of 12 ms?
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