A body of mass 2 kg begins to move under the influence of time dependent force F = (2ti + 6t^2j) N, where i and j are unit vectors along x and y-axis respectively. The power produced by the force at t = 2 s is _______ W.

The correct answer is Option 200. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q49 – JEE-MAIN 2026

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Home Physics Work, Energy & PowerQuestion #647

A body of mass

2

kg begins to move under the influence of time dependent force

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

N, where

\hat{i}

and

\hat{j}

are unit vectors along x and y-axis respectively. The power produced by the force at

t = 2

s is _______ W.

Enter Calculated Numerical Value:

Clue 1 of 3: Understand the relationship between force, mass, acceleration, velocity, and power

Power is the rate at which work is done, which can be expressed as the dot product of force and velocity.

🧠 Full Solution Path

Step 1: Determine acceleration and velocity as functions of time✦ Active

Given the force $\vec{F} = (2 t \hat{i} + 6 t^{2} \hat{j})$ N and mass $m = 2$ kg. According to Newton's second law, acceleration is $\vec{a} (t) = \frac{\vec{F} (t)}{m}$ .

\vec{a} (t) = \frac{1}{2} (2 t \hat{i} + 6 t^{2} \hat{j}) = (t \hat{i} + 3 t^{2} \hat{j}) {m/s}^{2}

Since the body "begins to move", its initial velocity $\vec{v} (0) = \vec{0}$ . Velocity is the integral of acceleration with respect to time.

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

Step 2: Calculate force and velocity at

t = 2

s○ Expand

Substitute $t = 2$ s into the expressions for force and velocity.

\vec{F} (2) = (2 (2) \hat{i} + 6 (2)^{2} \hat{j}) = (4 \hat{i} + 6 (4) \hat{j}) = (4 \hat{i} + 24 \hat{j}) N

\vec{v} (2) = (\frac{(2)^{2}}{2} \hat{i} + (2)^{3} \hat{j}) = (\frac{4}{2} \hat{i} + 8 \hat{j}) = (2 \hat{i} + 8 \hat{j}) m/s

Step 3: Compute the instantaneous power at

t = 2

s○ Expand

The instantaneous power $P$ is the dot product of the force and velocity vectors.

P (2) = \vec{F} (2) \cdot \vec{v} (2) = (4 \hat{i} + 24 \hat{j}) \cdot (2 \hat{i} + 8 \hat{j})

P (2) = (4) (2) + (24) (8) = 8 + 192 = 200 W

💡 Teacher's Secret Hint

Ensure to perform the dot product correctly by multiplying corresponding components and summing them.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Physics Question 49 – JEE-MAIN 2026

Clue 1 of 3: Understand the relationship between force, mass, acceleration, velocity, and power

🧠 Full Solution Path