(B) The instantaneous power $P_0$ is given by $P_0 = Fv$.Since $F = ma = m(dv/dt)$,we can write $P_0 = mv(dv/dt)$.Rearranging the terms,we get $P_0 dt

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) The instantaneous power $P_0$ is given by $P_0 = Fv$.Since $F = ma = m(dv/dt)$,we can write $P_0 = mv(dv/dt)$.Rearranging the terms,we get $P_0 dt = mv dv$.Integrating both sides from $t=0$ to $t$ and $v=0$ to $v$:$\int_0^t P_0 dt = \int_0^v mv dv$$P_0 t = \frac{1}{2}mv^2$.Solving for $v$,we get $v = \sqrt{\frac{2P_0 t}{m}}$.Therefore,$v \propto \sqrt{t}$ or $v \propto t^{1/2}$.

Class 11 Physics Work, Energy, Power and Collision Power

Medium

$A$ car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_0$. The instantaneous velocity of this car is proportional to

AIPMT 2012 All AIPMT

A
$t^2P_0$
B
$t^{1/2}$
C
$t^{3/2}$
D
$t/\sqrt{m}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Work, Energy, Power and Collision

Subtopic

Power

Previous Year

AIPMT 2012 Paper All AIPMT years →

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

DifficultJEE MAIN 2025

View Solution

From a waterfall,water is falling down at the rate of $100 \ kg/s$ on the blades of a turbine. If the height of the fall is $100 \ m$,then the power delivered to the turbine is approximately equal to ........... $kW$.

Medium

View Solution

$A$ bead of mass $400 \ g$ is moving along a straight line under a force that delivers a constant power $1.2 \ W$ to the bead. If the bead is initially at rest,the speed it attains after $6 \ s$ in $m \ s^{-1}$ is:

EasyAP EAMCET 2022

View Solution

Assume the aerodynamic drag force on a car is proportional to its speed. If the power output from the engine is doubled,then the maximum speed of the car:

Medium

View Solution

The force acting on a particle moving in a straight line varies with the velocity of the particle as $F = \frac{K}{v}$,where $K$ is a constant. The work done by this force in time $t$ is

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_0$. The instantaneous velocity of this car is proportional to

Similar Questions

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

From a waterfall,water is falling down at the rate of $100 \ kg/s$ on the blades of a turbine. If the height of the fall is $100 \ m$,then the power delivered to the turbine is approximately equal to ........... $kW$.

$A$ bead of mass $400 \ g$ is moving along a straight line under a force that delivers a constant power $1.2 \ W$ to the bead. If the bead is initially at rest,the speed it attains after $6 \ s$ in $m \ s^{-1}$ is:

Assume the aerodynamic drag force on a car is proportional to its speed. If the power output from the engine is doubled,then the maximum speed of the car:

The force acting on a particle moving in a straight line varies with the velocity of the particle as $F = \frac{K}{v}$,where $K$ is a constant. The work done by this force in time $t$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module