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

The correct answer is Option 2. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q28 – JEE-MAIN 2025

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Home Physics Work, Energy & PowerQuestion #659

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:

Clue 1 of 3: Definition of Power

Power is the rate at which work is done, and for a force acting on an object, it is given by the dot product of the force and the velocity of the object.

🥷

Ninja Strategy•Dimensional Analysis of Time Exponents

By analyzing how the time variable $t$ propagates through the equations for acceleration, velocity, and power, one can determine the expected exponents of $t$ in the final power expression, eliminating options with incorrect time dependencies.

🧠 Full Solution Path

Step 1: Calculate Acceleration and Velocity✦ Active

Given mass $m = 1000 g = 1 kg$ and force $\vec{F} = (2 t \hat{i} + 3 t^{2} \hat{j}) N$ . Using Newton's second law, $\vec{a} = \frac{\vec{F}}{m}$ .

\vec{a} = \frac{(2 t \hat{i} + 3 t^{2} \hat{j})}{1} = (2 t \hat{i} + 3 t^{2} \hat{j}) {m/s}^{2}

Assuming the object starts from rest (initial velocity is zero), integrate acceleration to find velocity $\vec{v} = \int \vec{a} d t$ .

\vec{v} = \int (2 t \hat{i} + 3 t^{2} \hat{j}) d t = (t^{2} \hat{i} + t^{3} \hat{j}) m/s

Step 2: Calculate Power○ Expand

The instantaneous power generated by the force is given by the dot product of the force vector and the velocity vector, $P = \vec{F} \cdot \vec{v}$ .

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

Perform the dot product:

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

Step 3: Final Answer○ Expand

The power generated by the force at time $t$ is $(2 t^{3} + 3 t^{5}) W$ . Comparing this with the given options, option 2 matches the result.

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Physics Question 28 – JEE-MAIN 2025

Clue 1 of 3: Definition of Power

🧠 Full Solution Path