Grade 11Mechanics

PLEASE ANSWER ASAP(TEST TODAY!)
Acceleration of a particle moving rectilinearly is a=4-2x.It is at instantaneous rest at x=0.At what position x(in m)will the particle again come to instantaneous rest?

MANAS GOEL

8 Years agoGrade 11

1 Answer

HIMANSHU SHEKHAR DAS

Approved Tutor Answer8 Years ago

as the relation is give in x so we have to find the differential relation between a, dv,dx

we know that acceleration is equal to rate of instantaneous change of velocity.

so a=dv/dt

multiplying dx in both numerator and denominator, we get a= (dv/dt)(dx/dx)

we know that dx/dt is nothing but velocity so we get a important relation that a=v*dv/dx

so v*dv/dx=4-2x

=> vdv=4-2x

integrating both sides and putting appropriate limits at x=0 the body was at instantaneous rest, so v=0 and let at a general velocity v the position vector is x.

$\int_{0}^{v}$ vdv = $\int_{0}^{x}$ xdx

=> v²/2 = 4x – x²

=> v²= 8x – 2x²

we know that at instantneous rest the velocity is 0

so v²is also 0

=> 8x=2x² => x=0 m or x=4 m

so the body comes to instantaneous rest again at x=4 m

thanks

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PLEASE ANSWER ASAP(TEST TODAY!)Acceleration of a particle moving rectilinearly is a=4-2x.It is at instantaneous rest at x=0.At what position x(in m)will the particle again come to instantaneous rest?

MANAS GOEL

1 Answer

HIMANSHU SHEKHAR DAS

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PLEASE ANSWER ASAP(TEST TODAY!)
Acceleration of a particle moving rectilinearly is a=4-2x.It is at instantaneous rest at x=0.At what position x(in m)will the particle again come to instantaneous rest?

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