JEE Main 2025 Apr 7 Shift 1, Physics Q18: Introduction

JEE Main2025Apr 7, Shift 1Physics

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

A
$(2 t^{2} + 3 t^{3})$ W
B
$(2 t^{2} + 18 t^{3})$ W
C
$(3 t^{3} + 5 t^{5})$ W
D
$(2 t^{3} + 3 t^{5})$ W

Solution

Given $m = 1000$ g $= 1$ kg, so the acceleration equals the force numerically:

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

Integrate to get velocity (starting from rest at $t = 0$ ):

$v = \int_{0}^{t} a d t^{'} = t^{2} \hat{i} + t^{3} \hat{j}$

Power $P = F \cdot v$ :

$P = (2 t \hat{i} + 3 t^{2} \hat{j}) \cdot (t^{2} \hat{i} + t^{3} \hat{j}) = 2 t \cdot t^{2} + 3 t^{2} \cdot t^{3} = 2 t^{3} + 3 t^{5}$

$∴$ Option (4).

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JEE Main 2025 Apr 7 Shift 1, Physics Q18: Introduction

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