A body starts from rest,under the action of a | vedclass

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

Question

(C) Given,Power $(P) =$ constant.Kinetic Energy $(KE) = \frac{1}{2} m v^{2}$.We know that,$P = \frac{d(KE)}{dt} = \frac{d}{dt} (\frac{1}{2} m v^{2}) =

Vedclass · Accepted Answer

$s=a t^{3 / 2}, a$ is a constant

Vedclass · Answer

(C) Given,Power $(P) =$ constant.Kinetic Energy $(KE) = \frac{1}{2} m v^{2}$.We know that,$P = \frac{d(KE)}{dt} = \frac{d}{dt} (\frac{1}{2} m v^{2}) = m v \frac{dv}{dt}$.Since $P$ is constant,$m v \frac{dv}{dt} = P$.Integrating both sides with respect to time $t$:$\int m v dv = \int P dt \Rightarrow \frac{1}{2} m v^{2} = P t$ (assuming initial velocity is $0$ at $t=0$).$v^{2} = \frac{2 P}{m} t \Rightarrow v = \sqrt{\frac{2 P}{m}} t^{1/2}$.Since $v = \frac{ds}{dt}$,we have $\frac{ds}{dt} = \sqrt{\frac{2 P}{m}} t^{1/2}$.Integrating with respect to $t$:$s = \int \sqrt{\frac{2 P}{m}} t^{1/2} dt = \sqrt{\frac{2 P}{m}} \cdot \frac{t^{3/2}}{3/2} = \frac{2}{3} \sqrt{\frac{2 P}{m}} t^{3/2}$.Thus,$s \propto t^{3/2}$,which means $s = a t^{3/2}$ where $a$ is a constant.

$A$ body starts from rest,under the action of an engine working at a constant power and moves along a straight line. The displacement $s$ is given as a function of time $t$ as:

Similar Questions

An electric motor exerts a force of $40 N$ on a cable and pulls it by a distance of $30 m$ in one minute. The power supplied by the motor (in Watts) is

An automatic gun fires $360$ bullets per minute with a speed of $360 \,km/h$. If each bullet weighs $20 \,g$,the power of the gun is (in $\,W$)

Water falls on the blades of a turbine at a rate of $100 \ kg/s$ from a height of $100 \ m$. The power generated is . . . . . . $kW$.

$A$ car of mass $m$ is accelerating on a level smooth road under the action of a single force $F$. The power delivered to the car is constant and equal to $P$. If the velocity of the car at an instant is $v$,then after travelling how much distance does its velocity become double?

An automobile of mass $m$ accelerates starting from the origin and is initially at rest,while the engine supplies constant power $P$. The position $x$ as a function of time $t$ is given by:

Vedclass Test Series

Exam Paper Generator

Online Exam Module