An object of mass 1000 g experiences a time dependent force . The power generated by the force at time t is: [2025]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
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: [2025]

1 $(2 t^{3} + 3 t^{3}) W$

2 $(2 t^{2} + 18 t^{3}) W$

3 $(3 t^{3} + 5 t^{5}) W$

4 $(2 t^{3} + 3 t^{5}) W$

Ans.
(4)

m = 1000 gram = 1 kg

$\vec{F} = (2 t \hat{i} + 3 t^{2} \hat{j})$

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

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

$\Rightarrow \vec{v} = t^{2} \hat{i} + t^{3} \hat{j}$

Power, $P = \vec{F} \cdot \vec{v}$

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

$P = (2 t^{3} + 3 t^{5}) W$

Want Us to Email you About Special Offers & Updates?