A body of mass 4 kg is placed on a plane at a point P having coordinate (3,4) m. Under the action of force ⃗F=(2̂i+3̂j) N, it moves to a new point Q having coordinates (6,10) m in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of

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(2) 6 : 13. Displacement ⃗d=(6-3)̂i+(10-4)̂j=3̂i+6̂j; work W=⃗F·⃗d=6+18=24 J. Average power: (24)/4=6 W. Instantaneous power at 4 s, taking the body to start from rest so ⃗v=(⃗F)/mt=(2̂i+3̂j) m/s: P=⃗F·⃗v=4+9=13 W. Ratio 6:13. (Strictly, a start from rest would give a displacement of 4̂i+6̂j, not the stated 3̂i+6̂j; the key follows the working above.)

A body of mass 4 kg is placed on a plane at a point P having coordinate (3,4) m. Under the action of force ⃗F=(2̂i+3̂j) N, it moves to a new point Q having coordinates (6,10) m in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of

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