Power supplied to a particle of mass 2, kg va | vedclass

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

Question

(C) Given: Mass $m = 2\, kg$,Power $P = \frac{3t^2}{2}$,and initial velocity $v(0) = 0$.We know that power $P = F \cdot v = (m \cdot a) \cdot v = m \c

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) Given: Mass $m = 2\, kg$,Power $P = \frac{3t^2}{2}$,and initial velocity $v(0) = 0$.We know that power $P = F \cdot v = (m \cdot a) \cdot v = m \cdot v \cdot \frac{dv}{dt}$.Substituting the given values: $2 \cdot v \cdot \frac{dv}{dt} = \frac{3t^2}{2}$.Rearranging the terms: $v \cdot dv = \frac{3t^2}{4} \cdot dt$.Integrating both sides from $t = 0$ to $t = 2$ and $v = 0$ to $v = V$:$\int_{0}^{V} v \, dv = \int_{0}^{2} \frac{3t^2}{4} \, dt$.$\left[ \frac{v^2}{2} \right]_{0}^{V} = \frac{3}{4} \left[ \frac{t^3}{3} \right]_{0}^{2}$.$\frac{V^2}{2} = \frac{1}{4} \cdot (2^3 - 0^3) = \frac{8}{4} = 2$.$V^2 = 4$,which gives $V = 2\, m/s$.

Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{3t^2}{2} \, W$. Here,$t$ is in $s$. If the velocity of the particle at $t = 0$ is $v = 0$,the velocity of the particle at time $t = 2\, s$ will be ............ $m/s$.

Similar Questions

$A$ car of mass $m$ is driven with constant power $P$. If it starts from rest,find its velocity $v$ after traveling a distance $x$.

If a force $F$ is applied on a body and it moves with a velocity $v$,the power will be

$A$ man is riding a cycle with a velocity of $7.2 \text{ km/hr}$ up a hill having a slope of $1$ in $20$. The total mass of the man and the cycle is $100 \text{ kg}$. The power of the man is ............ $\text{W}$. (in $\text{ W}$)

$A$ body of mass $m$ starts from rest and acquires a velocity $v$ in time $t$ under the action of a constant force $F$. The instantaneous power delivered to the body at time $t$ is:

$A$ pump on the ground floor can pump up water to fill a tank of volume $30 \ m^3$ in $15 \ minutes$. If the tank is $40 \ m$ above the ground and the efficiency of the pump is $30\%$,then the electric power consumed by the pump is ....... $kW$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module