An object is moving in a straight line under | vedclass

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

Question

(B) Power $P$ is defined as the rate of doing work,given by $P = F \cdot v$.Since $F = m \cdot a = m \frac{dv}{dt}$,we have $P = m \frac{dv}{dt} \cdot

Vedclass · Accepted Answer

$v \propto t^{\frac{1}{2}}$

Vedclass · Answer

(B) Power $P$ is defined as the rate of doing work,given by $P = F \cdot v$.Since $F = m \cdot a = m \frac{dv}{dt}$,we have $P = m \frac{dv}{dt} \cdot v$.Rearranging the terms,we get $P \cdot dt = m \cdot v \cdot dv$.Integrating both sides,$\int_{0}^{t} P \cdot dt = \int_{0}^{v} m \cdot v \cdot dv$.Since $P$ and $m$ are constant,$P \cdot t = m \cdot \frac{v^2}{2}$.Solving for $v$,we get $v^2 = \frac{2Pt}{m}$,which implies $v = \sqrt{\frac{2P}{m}} \cdot t^{\frac{1}{2}}$.Therefore,$v \propto t^{\frac{1}{2}}$.

An object is moving in a straight line under the influence of a source of constant power. If $v$ and $t$ are velocity and time respectively,then

Similar Questions

$A$ body of mass $2 \ kg$ begins to move under the action of a time-dependent force given by $\overrightarrow{F} = (6t \hat{i} + 6t^2 \hat{j}) \ N$. The power developed by the force at time $t$ is given by:

$A$ vehicle of mass $m$ starts from rest and accelerates. If the engine delivers a constant power $p$,what is the velocity of the vehicle at time $t$?

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

$A$ car of mass $2000 \ kg$ is lifted by a crane through a distance of $30 \ m$ in $1 \ minute$. $A$ second crane does the same in $2 \ minutes$. The power supplied by each crane is respectively:

$A$ body moves along a straight line under the action of a constant power delivered by an engine. The distance covered by the body in time $t$ is proportional to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module