A body is moved along a straight line by a ma | vedclass

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

Question

(C) Given that power $P$ is constant. We know that $P = Fv = mav = m \left( \frac{dv}{dt} \right) v$. Integrating this expression: $\frac{P}{m} dt = v

Vedclass · Accepted Answer

$t^{3/2}$

Vedclass · Answer

(C) Given that power $P$ is constant. We know that $P = Fv = mav = m \left( \frac{dv}{dt} \right) v$. Integrating this expression: $\frac{P}{m} dt = v dv$. Integrating both sides: $\int \frac{P}{m} dt = \int v dv \implies \frac{P}{m} t = \frac{v^2}{2}$. Thus,$v^2 = \frac{2P}{m} t$,which gives $v = \sqrt{\frac{2P}{m}} t^{1/2}$. Since $v = \frac{ds}{dt}$,we have $ds = \sqrt{\frac{2P}{m}} t^{1/2} dt$. Integrating with respect to $t$: $s = \int \sqrt{\frac{2P}{m}} t^{1/2} dt = \sqrt{\frac{2P}{m}} \left( \frac{t^{3/2}}{3/2} \right) = \sqrt{\frac{2P}{m}} \left( \frac{2}{3} t^{3/2} \right)$. Therefore,$s \propto t^{3/2}$.

$A$ 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

Similar Questions

Write a note on Power.

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

When a constant force is applied to a body moving with constant acceleration,power does not remain constant. For power to be constant,the force has to vary with speed as follows:

The power of a water pump is $4 \,kW$. If $g = 10 \,m/s^2$,the amount of water it can raise in $1 \,minute$ to a height of $20 \,m$ is ........... $litres$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module