A particle of mass M,starting from rest,under | vedclass

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

Question

(D) The particle starts from rest,so its initial velocity $u = 0$. Given acceleration $a$ is uniform,the velocity $V$ at time $T$ is given by $V = aT$

Vedclass · Accepted Answer

$\frac{1}{2} \left( \frac{MV^2}{T} \right)$

Vedclass · Answer

(D) The particle starts from rest,so its initial velocity $u = 0$. Given acceleration $a$ is uniform,the velocity $V$ at time $T$ is given by $V = aT$,which implies $a = \frac{V}{T}$. The force acting on the particle is $F = Ma = M \left( \frac{V}{T} \right)$. Power $P$ delivered to the particle is defined as $P = F \cdot V$. Substituting the values of $F$ and $V$: $P = \left( M \frac{V}{T} \right) \cdot V = \frac{MV^2}{T}$. However,the instantaneous power at time $T$ is $P = F \cdot V = (Ma) \cdot (aT) = Ma^2T$. Since $a = V/T$,$P = M(V/T)^2 T = \frac{MV^2}{T}$. Wait,let's re-evaluate: The work done $W = \Delta K = \frac{1}{2}MV^2$. Average power $P_{avg} = \frac{W}{T} = \frac{MV^2}{2T}$. Looking at the options,option $D$ represents the average power delivered to the particle.

$A$ particle of mass $M$,starting from rest,undergoes uniform acceleration. If the speed acquired in time $T$ is $V$,the power delivered to the particle is

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 ......... $J/s$.

$A$ car of mass $2000 \ kg$ is accelerating from rest. If its engine is supplying a constant power of $10 \ kW$,then the velocity of the car at a time of $10 \ s$ is: (in $m \ s^{-1}$)

If $\overrightarrow{F} = (60 \hat{i} + 15 \hat{j} - 3 \hat{k}) \; N$ and $\overrightarrow{V} = (2 \hat{i} - 4 \hat{j} + 5 \hat{k}) \; m/s$,then the instantaneous power is: (in $; W$)

$A$ force applied by an engine of a train of mass $2.05 \times 10^6 \; kg$ changes its velocity from $5 \; m/s$ to $25 \; m/s$ in $5$ minutes. The power of the engine is ........... $MW$.

Water is falling on the blades of a turbine from a height of $25 \ m$. $3 \times 10^3 \ kg$ of water pours on the blade per minute. If the whole of energy is transferred to the turbine,the power delivered is: (in $W$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module