A body is moved along a straight line by an e | vedclass

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

Question

(C) Power $P$ is given by $P = Fv$, where $F$ is force and $v$ is velocity.Since $P$ is constant, $Fv = 	ext{constant}$.Using Newton's second law, $F

Vedclass · Accepted Answer

$t^{3/2}$

Vedclass · Answer

(C) Power $P$ is given by $P = Fv$, where $F$ is force and $v$ is velocity.Since $P$ is constant, $Fv = 	ext{constant}$.Using Newton's second law, $F = ma$, so $(ma)v = 	ext{constant}$.Since $a = \frac{dv}{dt}$ and $v = \frac{ds}{dt}$, we have $m \left(\frac{dv}{dt}ight)v = P$.$mv \, dv = P \, dt$.Integrating both sides: $\int mv \, dv = \int P \, dt \implies \frac{1}{2}mv^2 = Pt$.Thus, $v^2 \propto t$, which means $v \propto t^{1/2}$.Since $v = \frac{ds}{dt}$, we have $\frac{ds}{dt} \propto t^{1/2}$.Integrating with respect to time: $s \propto \int t^{1/2} \, dt$.$s \propto t^{3/2}$.

$A$ body is moved along a straight line by an engine which delivers a constant power. The distance moved by the body in time $t$ is proportional to:

Similar Questions

$A$ particle moves with a velocity $\vec v = 6\hat i - 4\hat j + 3\hat k \, m/s$ under the influence of a constant force $\vec F = 20\hat i + 15\hat j - 5\hat k \, N$. The instantaneous power applied to the particle is ......... $J/s$.

An electric motor produces a tension of $4500 N$ in a wire and the reel winds at a rate of $2 ms^{-1}$. What is the power of the electric motor?

$A$ body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time $t$ is proportional to

$A$ body of mass $2\, kg$ is driven by an engine delivering a constant power $1\, J/s$. The body starts from rest and moves in a straight line. After $9$ seconds,the body has moved a distance (in $m$):

The machine gun fires $240$ bullets per minute. If the mass of each bullet is $10 \ g$ and the velocity of the bullets is $600 \ ms^{-1}$,the power (in $kW$) of the gun is

Vedclass Test Series

Exam Paper Generator

Online Exam Module