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JEE Main 20264 AprilMorning Shift
Exam
JEE Main
Year
2026
Date
4 April
Shift
Morning Shift
Subject
Physics
Chapter
Work, Power and Energy

JEE Main 2026 · 4 April · Morning Shift · Physics · Work, Power and Energy

A body of mass 2 kg begins to move under the influence of time...

A body of mass 22 kg begins to move under the influence of time dependent force F⃗=(2ti^+6t2j^)\vec{F} = (2t\hat{i} + 6t^2\hat{j}) N, where i^\hat{i} and j^\hat{j} are unit vectors along xx and yy-axis respectively. The power produced by the force at t=2t = 2 s is _____ W.

Correct answer

0

Step-by-step solution

Given F⃗=(2ti^+6t2j^)\vec{F} = (2t\hat{i} + 6t^2\hat{j}) N and m=2m = 2 kg.

Acceleration of the body is a⃗=F⃗m=2ti^+6t2j^2=ti^+3t2j^\vec{a} = \dfrac{\vec{F}}{m} = \dfrac{2t\hat{i} + 6t^2\hat{j}}{2} = t\hat{i} + 3t^2\hat{j} m/s2^2.

Since the body begins to move from rest, its velocity at time tt is given by v⃗=∫a⃗dt=∫(ti^+3t2j^)dt=t22i^+t3j^\vec{v} = \int \vec{a} dt = \int (t\hat{i} + 3t^2\hat{j}) dt = \dfrac{t^2}{2}\hat{i} + t^3\hat{j} m/s.

At t=2t = 2 s, the force is F⃗=2(2)i^+6(2)2j^=4i^+24j^\vec{F} = 2(2)\hat{i} + 6(2)^2\hat{j} = 4\hat{i} + 24\hat{j} N.

At t=2t = 2 s, the velocity is v⃗=(2)22i^+(2)3j^=2i^+8j^\vec{v} = \dfrac{(2)^2}{2}\hat{i} + (2)^3\hat{j} = 2\hat{i} + 8\hat{j} m/s.

Power produced by the force is P=F⃗⋅v⃗=(4i^+24j^)⋅(2i^+8j^)P = \vec{F} \cdot \vec{v} = (4\hat{i} + 24\hat{j}) \cdot (2\hat{i} + 8\hat{j}).

P=(4×2)+(24×8)=8+192=200P = (4 \times 2) + (24 \times 8) = 8 + 192 = 200 W.

Answer: 200200
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