A body at rest is moved along a horizontal st | vedclass

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

Question

(C) Given that the power $P$ delivered by the machine is constant.The work done by the machine in time $t$ is $W = P \cdot t$.According to the work-en

Vedclass · Accepted Answer

$t^{3/2}$

Vedclass · Answer

(C) Given that the power $P$ delivered by the machine is constant.The work done by the machine in time $t$ is $W = P \cdot t$.According to the work-energy theorem,the work done is equal to the change in kinetic energy: $W = \Delta K = \frac{1}{2} m v^2 - 0 = \frac{1}{2} m v^2$.Equating the two,we get $\frac{1}{2} m v^2 = P \cdot t$.This implies $v^2 \propto t$,or $v \propto t^{1/2}$.Since velocity $v = \frac{dx}{dt}$,we have $\frac{dx}{dt} = k \cdot t^{1/2}$ (where $k$ is a constant).Integrating with respect to time $t$ to find the distance $x$:$x = \int k \cdot t^{1/2} dt = k \cdot \frac{t^{1/2 + 1}}{1/2 + 1} = k \cdot \frac{t^{3/2}}{3/2}$.Therefore,$x \propto t^{3/2}$.

$A$ 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 :

Similar Questions

Show that the rate of change of kinetic energy is a power.

An elevator lifts a load of $500 \ kg$ with a constant speed of $0.4 \ m/s$. What is the minimum horsepower $(H.P.)$ of the motor required?

An engine is dragging a mass of $5000 \ kg$ with a velocity of $5 \ ms^{-1}$ along a smooth inclined plane of inclination $1$ in $50$. Then the power of the engine is (in $kW$)

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.

$A$ particle moves with a velocity $\vec{v} = 5\hat{i} - 3\hat{j} + 6\hat{k} \text{ m/s}$ under the influence of a constant force $\vec{F} = 10\hat{i} + 10\hat{j} + 20\hat{k} \text{ N}$. The instantaneous power will be ............... $\text{J/s}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module