A body of mass 1 kg begins to move under the | vedclass

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

Question

(C) Given force: $\vec{F} = t \hat{i} + 3t^2 \hat{j} \ N$ and mass $m = 1 \ kg$.Using Newton's second law,$\vec{F} = m \vec{a} = m \frac{d\vec{v}}{dt}

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(C) Given force: $\vec{F} = t \hat{i} + 3t^2 \hat{j} \ N$ and mass $m = 1 \ kg$.Using Newton's second law,$\vec{F} = m \vec{a} = m \frac{d\vec{v}}{dt}$.Since $m = 1 \ kg$,$\frac{d\vec{v}}{dt} = t \hat{i} + 3t^2 \hat{j}$.Integrating with respect to time $t$ (assuming initial velocity is zero at $t=0$): $\vec{v} = \int (t \hat{i} + 3t^2 \hat{j}) dt = \frac{t^2}{2} \hat{i} + t^3 \hat{j} \ m/s$.Power $P$ is given by the dot product of force and velocity: $P = \vec{F} \cdot \vec{v}$.$P = (t \hat{i} + 3t^2 \hat{j}) \cdot (\frac{t^2}{2} \hat{i} + t^3 \hat{j}) = \frac{t^3}{2} + 3t^5$.At $t = 2 \ s$,$P = \frac{2^3}{2} + 3(2^5) = \frac{8}{2} + 3(32) = 4 + 96 = 100 \ W$.

$A$ body of mass $1 \ kg$ begins to move under the action of a time-dependent force $\vec{F} = (t \hat{i} + 3t^2 \hat{j}) \ N$,where $\hat{i}$ and $\hat{j}$ are the unit vectors along the $x$ and $y$ axes. The power developed by the above force at time $t = 2 \ s$ will be $.............. \ W$.

Similar Questions

$A$ body moves along a straight line due to a constant power delivered by a machine. The distance covered by the body in time $t$ is proportional to:

$A$ water pump rated $600 W$ has an efficiency of $95 \%$. If it is used to raise water through a vertical distance of $60 m$,what is the volume of water drawn in $20$ minutes (in $m^3$)? [Use density of water $= 1000 kg/m^3$,$g = 10 m/s^2$]

$A$ crane of efficiency $80 \%$ is used to lift $8000 \ kg$ of coal from a mine of depth $108 \ m$. If the time taken by the crane to lift the coal is one hour, then the power of the crane (in $kW$) is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)

$A$ body is moved along a straight line by an engine which delivers a constant power. The distance moved by the body in time $t$ is proportional to:

$A$ 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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module