Q.

A body of mass 1kg begins to move under the action of a time dependent force F→=(2t i^+3t2 j^)N,where i^ and j^ are unit vectors along x and yaxis. What power will be developed by the force at the time t ?

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a

2t3+3t4W

b

2t3+3t5W

c

2t2+3t3W

d

2t2+4t4W

answer is B.

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Detailed Solution

Here, F→=2t i^+3t2 j^N, m=1 kg Velocity of the body at time tv→=∫a→dt=∫2t i^+3t2 j^dt=t2 i^+t3 j^   ms-1∴ Power developed by the force at time t,P=F→·v→=2ti^+3t2j^·t2i^+t3j^ W=2t3+3t5 W
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A body of mass 1kg begins to move under the action of a time dependent force F→=(2t i^+3t2 j^)N,where i^ and j^ are unit vectors along x and yaxis. What power will be developed by the force at the time t ?