A body is moving unidirectionally under the i | vedclass

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

Question

(C) Given that power $P$ is constant.Since $P = F \cdot v = m \cdot a \cdot v = m \cdot \frac{dv}{dt} \cdot v$,we have $m \cdot v \cdot \frac{dv}{dt}

Vedclass · Accepted Answer

$t^{3/2}$

Vedclass · Answer

(C) Given that power $P$ is constant.Since $P = F \cdot v = m \cdot a \cdot v = m \cdot \frac{dv}{dt} \cdot v$,we have $m \cdot v \cdot \frac{dv}{dt} = P$.Integrating both sides with respect to time: $\int m \cdot v \cdot dv = \int P \cdot dt$.This gives $\frac{1}{2} m v^2 = P \cdot t$,which implies $v^2 \propto t$,or $v \propto t^{1/2}$.Since velocity $v = \frac{ds}{dt}$,we have $\frac{ds}{dt} \propto t^{1/2}$.Integrating with respect to time: $s = \int t^{1/2} dt = \frac{t^{3/2}}{3/2} = \frac{2}{3} t^{3/2}$.Therefore,displacement $s \propto t^{3/2}$.

$A$ body is moving unidirectionally under the influence of a constant power source. Its displacement in time $t$ is proportional to :

Similar Questions

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 $\,W$)

$A$ man of mass $80 \ kg$ climbs a ladder of height $6 \ m$ in $10 \ s$. What is the average power generated by him in $HP$ (Horsepower)?

$A$ 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:

The average work done by a human heart while it beats once is $0.5 \, J$. Calculate the power used by the heart if it beats $72$ times in a minute.

Vedclass Test Series

Exam Paper Generator

Online Exam Module