Average Velocity and instantaneous velocity

Average Velocity and instantaneous velocity

Credit: Vasck.cz(Motion)

Introduction : We have studied about Motion in One dimension .i.e motion in a straight line (Rectilinear motion). Motion of a particle in straight line is governed by three kinematical equation (v = u + at) , v² = u² + 2as), (s = ut + 1/2 at²) which gives the relation between position, displacement, velocity and acceleration. Now in this topic we are going to learn in detail about position vector, displacement, velocity and acceleration in 2 dimension.

Position vector : Let us understand the position vector in 2 dimension. From the fig below, the position vector at time t₁ is OP = r and position vector at time t2 is OQ = r'. The change in positionn vector i.e , PQ is ∆r = r' - r . 

Thus mathematically, 

r = x î + y ĵ

r' = x' î + y' ĵ    

From Triangle law of vector addition,

OP + PQ = OR

r + ∆r = r'

∆r = r' - r

∆r = (x' î + y' ĵ ) - (  x î + y ĵ  )

∆r = ( x'  - x )  î + ( y' - y ) ĵ -----(A)

Equation (A) gives change in position vector  in 2 dimension.

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Average velocity

The average velocity of  a particle performing motion in a plane is given by,

The instantaneous velocity of  a particle performing motion in a plane is given by,

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_{Average acceleration}

_{From above diagram and expression}

_{Mathematically, average acceleration is given by,}

_{Mathematically, instantaneous acceleration is given by,}

_{│<<<Motion in a plane│   │Projectile Motion>>>│} 

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