A body of mass 2 kg begins to… - JEE Main 2026 Physics PYQ

JEE Main 2026 — Physics Mechanics

2026integermedium

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.

Official previous-year question

Held on 4 Apr 2026 · Verified 6 Jul 2026.

Did you get this right?

Solution

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

Acceleration of the body is $\vec{a} = \dfrac{\vec{F}}{m} = \dfrac{2t\hat{i} + 6t^2\hat{j}}{2} = t\hat{i} + 3t^2\hat{j}$ m/s $^2$ .

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

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

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

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

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

Answer: $200$

Your note

JEE Main Mechanics in other years

Mechanics 2025 Mechanics 2024 Mechanics 2023 Mechanics 2022 Mechanics 2021 Mechanics 2020 Mechanics 2019 Mechanics 2018 Mechanics 2017 Mechanics 2016 Mechanics 2015 Mechanics 2014

Keep practicing Mechanics

Work through every JEE Main Mechanics PYQ, year by year.

Browse all Physics topics

Solution

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

Acceleration of the body is $\vec{a} = \dfrac{\vec{F}}{m} = \dfrac{2t\hat{i} + 6t^2\hat{j}}{2} = t\hat{i} + 3t^2\hat{j}$ m/s $^2$ .

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

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

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

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

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

Answer: $200$

Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

More JEE Main Mechanics questions

Other Physics topics for JEE Main

Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Mechanics

Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

More JEE Main Mechanics questions

Other Physics topics for JEE Main

Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Mechanics