A particle of mass m is driven by a machine t | vedclass

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

Question

(A) The power $P$ delivered to the particle is constant,so $P = k$.Since $P = \frac{dW}{dt}$,we have $dW = k dt$.Integrating both sides from $0$ to $t

Vedclass · Accepted Answer

$\sqrt {\frac{{mk}}{2}} \;{t^{ - \frac{1}{2}}}$

Vedclass · Answer

(A) The power $P$ delivered to the particle is constant,so $P = k$.Since $P = \frac{dW}{dt}$,we have $dW = k dt$.Integrating both sides from $0$ to $t$,we get $W = kt$.According to the work-energy theorem,the work done is equal to the change in kinetic energy:$W = \Delta K = \frac{1}{2}mv^2 - 0$.Equating the two expressions for $W$: $kt = \frac{1}{2}mv^2$,which gives $v = \sqrt{\frac{2kt}{m}}$.The acceleration $a$ is the derivative of velocity with respect to time:$a = \frac{dv}{dt} = \frac{d}{dt} \left( \sqrt{\frac{2k}{m}} t^{1/2} \right) = \sqrt{\frac{2k}{m}} \cdot \frac{1}{2} t^{-1/2} = \sqrt{\frac{k}{2mt}}$.The force $F$ acting on the particle is $F = ma$:$F = m \cdot \sqrt{\frac{k}{2mt}} = \sqrt{\frac{m^2 k}{2mt}} = \sqrt{\frac{mk}{2t}} = \sqrt{\frac{mk}{2}} t^{-1/2}$.

$A$ particle of mass $m$ is driven by a machine that delivers a constant power $k$ watts. If the particle starts from rest,the force on the particle at time $t$ is:

Similar Questions

Water is pumped from a depth of $10 \ m$ and delivered through a pipe of cross-section $10^{-2} \ m^2$. If it is needed to deliver a volume of $10^{-1} \ m^3$ per second,the power required will be ........ $kW$.

If the heart pumps $1 \ cc$ of blood in $1 \ s$ at a pressure of $20000 \ N/m^2$,find the power of the heart in $W$.

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of $2\, m/s$. The mass per unit length of water in the pipe is $100\, kg/m$. Calculate the power $W$ of the engine. (in $, W$)

If $\overrightarrow{F} = (60 \hat{i} + 15 \hat{j} - 3 \hat{k}) \; N$ and $\overrightarrow{V} = (2 \hat{i} - 4 \hat{j} + 5 \hat{k}) \; m/s$,then the instantaneous power is: (in $; W$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module