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

Physics · Work, Power & Energy

JEE Main 2025 — 7 April, Morning Shift — Question 48

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

Option A:
$\left(2 t^{2}+3 t^{3}\right) \mathrm{W}$
Option B:
$\left(3 t^{3}+5 t^{5}\right) \mathrm{W}$
Option C:
$\left(2 t^{2}+18 t^{3}\right) \mathrm{W}$
Option D:
$\left(2 t^{3}+3 t^{5}\right) \mathrm{W}$
Correct

Answer: D

Step-by-step solution

$m=1000$ gram $\vec{F}=\left(2 t \hat{i}+3 t^{2} \hat{j}\right)$

So, $\frac{d v}{d t}=\frac{F}{m}=\left(2 t \hat{i}+3 t^{2} \hat{j}\right)$

So $\int_{0}^{v} d v=\int_{0}^{t}\left(2 t \hat{i}+3 t^{2} \hat{j}\right) d t$

So $\quad v=\left(t \hat{i}+t^{3} \hat{j}\right)$ So power $=\vec{F} \cdot \vec{V}=2 t^{2}+3 t^{5}$

Answer key and solution verified before publishing.

Practise Work, Power & Energy

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2025
Paper: 7 April, Morning Shift
Subject: Physics
Chapter: Work, Power & Energy
Topic: Power