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An object of mass \(1000\mathrm{g}\) experiences a time dependent force \(\vec{\mathrm{F}}=\left(2\mathrm{t}\overset{^}{…

Q1

An object of mass \(1000\mathrm{g}\) experiences a time dependent force \(\vec{\mathrm{F}}=\left(2\mathrm{t}\overset{^}{\mathrm{i}}+3{\mathrm{t}}^{2}\overset{^}{\mathrm{j}}\right)\mathrm{N}\). The power generated by the force at time t is :

[JEE Main 2025, 7 Apr (Shift 1)]

a

\(\left(2{t}^{2}+3{t}^{3}\right)W\)

b

\(\left(2{t}^{2}+18{t}^{3}\right)\mathrm{W}\)

c

\(\left(3{t}^{3}+5{t}^{5}\right)W\)

d

\(\left(2{t}^{3}+3{t}^{5}\right)W\)

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