Question

A body of mass 2 kg begins to move under the action of a time dependent force given by \(\vec {F}=(6t\, \hat {i} + 6t^2\,\hat {j})N.\) The power developed by the force at the time t is given by:

(1) \((6t^4 + 9t ^5)W\)

(2) \((3t^3 + 6t ^5)W\)

(3) \((9t^5 + 6t ^3)W\)

(4) \((9t^3 +6t^5)W\)

Answer 1

(4) \((9t^3 +6t^5)W\)

\(\vec {F}=(6t\,\hat {i}+6t^2 \,\hat {j})N\)

\(\vec {F}=m\vec {a}=(6t\hat {i}+6t^2\hat {j})\)

\(\vec {a}=\frac {\vec{F}}{m}=(3t\hat {i}+3t^2\hat {j})\)

\(\vec {v}=\int ^t _0 \vec {a}dt= \frac {3t^2}{2}\hat {i}+t ^3 \hat {j}\)

\(P =\vec {F}.\vec{v}= (9t^3 +6t^5)W\)