An object of mass 1000 g experiences a time dependent force . The power generated by the force at time t is: [2025]

Question

An object of mass 1000 g experiences a time dependent force $\vec{F} = (2 t \hat{i} + 3 t^{2} \hat{j}) N$ . The power generated by the force at time t is: [2025]

Smart Achievers · Accepted Answer

(4)

m = 1000 gram = 1 kg

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

$\frac{d v}{d t} = \frac{F}{m} = (2 t \hat{i} + 3 t^{2} \hat{j})$

$\Rightarrow \int_{0}^{v} d v = \int_{0}^{t} (2 t \hat{i} + 3 t^{2} \hat{j}) d t$

$\Rightarrow \vec{v} = t^{2} \hat{i} + t^{3} \hat{j}$

Power, $P = \vec{F} \cdot \vec{v}$

$P = (2 t \hat{i} + 3 t^{2} \hat{j}) \cdot (t^{2} \hat{i} + t^{3} \hat{j})$

$P = (2 t^{3} + 3 t^{5}) W$

Solution

Q.
An object of mass 1000 g experiences a time dependent force $\vec{F} = (2 t \hat{i} + 3 t^{2} \hat{j}) N$ . The power generated by the force at time t is: [2025]

1 $(2 t^{3} + 3 t^{3}) W$

2 $(2 t^{2} + 18 t^{3}) W$

3 $(3 t^{3} + 5 t^{5}) W$

4 $(2 t^{3} + 3 t^{5}) W$

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Solution

Q. An object of mass 1000 g experiences a time dependent force F→=(2ti^+3t2j^)N. The power generated by the force at time t is: [2025]

1 (2t3+3t3)W

2 (2t2+18t3)W

3 (3t3+5t5)W

4 (2t3+3t5)W