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Question:

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

(2t^3+3t^4)W

(2t^2+4t^4)W

(2t^3+3t^5)W

(2t^2+3t^3)W

Solution:

Applying Newton's second law of motion, acceleration, →a=→F/m=2t^i+3t^2^j
Acceleration is defined as rate of change of velocity, →a=d→v/dt
→v=∫₀ᵗ→adt
→v=∫₀ᵗ(2t^i+3t^2^j)dt
→v=t^2^i+t^3^j
Power, P=→F.→v=(2t^i+3t^2^j) (t^2^i+t^3^j)
P=(2t^3+3t^5) W