Grade 12Mechanics

A PARTICLE OF MASS m IS MOVING ON A STRAIGHT LINE SUCH THAT ITS SPEED CHANGES WITH DISTANCE TRAVELLED AS v = b x^1/2 . THE WORK DONE BY NET FORCE ON THE PARTICLE DURING FIRST t seconds what ?

RAGINI SEIWAL

8 Years agoGrade 12

1 Answer

venkat

8 Years ago

Given,

Mass of the particle = m

Velocity varies linearly with distance travelled as

v=bx^1/2

Force acting on the body,

F=ma

F=m*dv/dt

F=m*(dv/dx)*(dx/dt) [Multiplying and dividing with ‘dx’]

F=mv*(dv/dx) [ $\because$ dx/dt=v]

F=mv*(d(bx^1/2)/dx)

F=m(bx^1/2)(bx^-1/2/2)

F=mb²/2

Distance moved by by the body in first ‘t’ seconds is given by

v=dx/dt

dt=dx/v

Integrating on both sides, we get

$\int_{}^{}$ dt= $\int$ dx/v

t=(1/b) $\int$ dx/(x^1/2)

t=(2/b)*x^1/2

t=(2x^1/2)/b

i.e., distance travelled by the body in first t seconds s=b²t²/4

Work done by the force on the body in first t seconds is given by

W=Fs

W={mb²/2}*{b²t²/4}

$\therefore$ Work done W=mb⁴t²/8

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A PARTICLE OF MASS m IS MOVING ON A STRAIGHT LINE SUCH THAT ITS SPEED CHANGES WITH DISTANCE TRAVELLED AS v = b x^1/2 . THE WORK DONE BY NET FORCE ON THE PARTICLE DURING FIRST t seconds what ?

RAGINI SEIWAL

1 Answer

venkat

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