A body of mass 2 kg begins to move under the influence of time dependent force $\vec{F}=(2t\hat{i}+6t^2\hat{j})$ 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.

JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Work, Power & Energy

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

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.

Answer: 200

Solution

The acceleration is

a = \frac{F}{m} = t \hat{i} + 3 t^{2} \hat{j}

. Starting from rest,

v = \int_{0}^{t} a d t = \frac{t ^{2}}{2} \hat{i} + t^{3} \hat{j}

, so at

t = 2

v = 2 \hat{i} + 8 \hat{j}

m/s and

F = 4 \hat{i} + 24 \hat{j}

N. The power is

P = F \cdot v = (4) (2) + (24) (8) = 8 + 192 = 200

JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Integer answer

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