JEE Main 2026 — Apr 4, Shift 1 — Physics solution

JEE Main2026Apr 4, Shift 1Physics

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.

Your answer

Solution

Acceleration: $a = \frac{F}{m} = t \hat{i} + 3 t^{2} \hat{j}$ m/s $^{2}$ .

Velocity from rest: $v (t) = \int_{0}^{t} a d t^{'} = \frac{t ^{2}}{2} \hat{i} + t^{3} \hat{j} .$

At $t = 2$ s: $v = 2 \hat{i} + 8 \hat{j}$ m/s and $F (2) = 4 \hat{i} + 24 \hat{j}$ N.

Power: $P = F \cdot v = 4 (2) + 24 (8) = 8 + 192 = 200$ W.

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